Download or read book An Introduction to Manifolds written by Loring W. Tu and published by Springer Science & Business Media. This book was released on 2010-10-05 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Download or read book Manifold Destiny written by Chris Maynard and published by Simon and Schuster. This book was released on 2008-11-18 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving new meaning to the term "fast food" Rest-stop grade F meat patty? Nah. Nuggets of reconstituted poultry bits? Pass. Deep-fried fish discus? No, really, thanks all the same. It's time to bid farewell to the roadside meal as you know it. Nearly twenty years ago, Chris Maynard and Bill Scheller opened the world's eyes to the beautym of car-engine gastronomy in the original Manifold Destiny. And now that another generation of both drivers and eaters has emerged, the cult classic is due for an overhaul. In this shiny, spanking-new edition, learn how to make s'mores in your Scion, poach fish in your Pontiac, even bust out a gourmet snack from under the hood of your Escalade. With step-by-step diagrams, crowd-pleasing recipes, and thorough instructions, now you can turn your car into a kitchen without ever crossing any golden arches. Hilarious, bizarre, and ultimately (seriously!) useful, Manifold Destiny is and always will be an unparalleled original. So, slap a ham steak under the hood of your car, hit the gas, and drive until you reach delicious -- which is in approximately fifty miles, depending on traffic.
Download or read book A New Construction of Homogeneous Quaternionic Manifolds and Related Geometric Structures written by Vicente Cortés and published by American Mathematical Soc.. This book was released on 2000 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $V = {\mathbb R}^{p,q}$ be the pseudo-Euclidean vector space of signature $(p,q)$, $p\ge 3$ and $W$ a module over the even Clifford algebra $C\! \ell^0 (V)$. A homogeneous quaternionic manifold $(M,Q)$ is constructed for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \wedge^2 W \rightarrow V$. If the skew symmetric vector valued bilinear form $\Pi$ is nondegenerate then $(M,Q)$ is endowed with a canonical pseudo-Riemannian metric $g$ such that $(M,Q,g)$ is a homogeneous quaternionic pseudo-Kahler manifold. If the metric $g$ is positive definite, i.e. a Riemannian metric, then the quaternionic Kahler manifold $(M,Q,g)$ is shown to admit a simply transitive solvable group of automorphisms. In this special case ($p=3$) we recover all the known homogeneous quaternionic Kahler manifolds of negative scalar curvature (Alekseevsky spaces) in a unified and direct way. If $p>3$ then $M$ does not admit any transitive action of a solvable Lie group and we obtain new families of quaternionic pseudo-Kahler manifolds. Then it is shown that for $q = 0$ the noncompact quaternionic manifold $(M,Q)$ can be endowed with a Riemannian metric $h$ such that $(M,Q,h)$ is a homogeneous quaternionic Hermitian manifold, which does not admit any transitive solvable group of isometries if $p>3$. The twistor bundle $Z \rightarrow M$ and the canonical ${\mathrm SO}(3)$-principal bundle $S \rightarrow M$ associated to the quaternionic manifold $(M,Q)$ are shown to be homogeneous under the automorphism group of the base. More specifically, the twistor space is a homogeneous complex manifold carrying an invariant holomorphic distribution $\mathcal D$ of complex codimension one, which is a complex contact structure if and only if $\Pi$ is nondegenerate. Moreover, an equivariant open holomorphic immersion $Z \rightarrow \bar{Z}$ into a homogeneous complex manifold $\bar{Z}$ of complex algebraic group is constructed. Finally, the construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \vee^2 W \rightarrow V$ a homogeneous quaternionic supermanifold $(M,Q)$ is constructed and, moreover, a homogeneous quaternionic pseudo-Kahler supermanifold $(M,Q,g)$ if the symmetric vector valued bilinear form $\Pi$ is nondegenerate.
Download or read book Introduction to Topological Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Download or read book Introduction to Smooth Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Download or read book Manifold Space written by Stephen Baxter and published by Del Rey. This book was released on 2003-12-16 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: “As always, [Stephen] Baxter plays with space and time with consummate skill. . . . He continues to be one of the leading writers of hard science fiction, and one of the most thought-provoking as well.”—Science Fiction Chronicle The year is 2020. Fueled by an insatiable curiosity, Reid Malenfant ventures to the far edge of the solar system, where he discovers a strange artifact left behind by an alien civilization: A gateway that functions as a kind of quantum transporter, allowing virtually instantaneous travel over the vast distances of interstellar space. What lies on the other side of the gateway? Malenfant decides to find out. Yet he will soon be faced with an impossible choice that will push him beyond terror, beyond sanity, beyond humanity itself. Meanwhile on Earth the Japanese scientist Nemoto fears her worst nightmares are coming true. Startling discoveries reveal that the Moon, Venus, even Mars once thrived with life—life that was snuffed out not just once but many times, in cycles of birth and destruction. And the next chilling cycle is set to begin again . . . “When the travel bug bites and usual planets don’t excite, perhaps it’s time to burst the bounds of this old solar system and really see the sights. . . . Baxter’s expansive new novel is just the ticket.”—The Washington Times “Breathtaking in its originality and scope.”—The Washington Post
Download or read book Manifold Time written by Stephen Baxter and published by Del Rey. This book was released on 2003-12-16 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Reading Manifold: Time is like sending your mind to the gym for a brisk workout. If you don’t feel both exhausted and exhilirated when you’re done, you haven’t been working hard enough.”—The New York Times Book Review The year is 2010. More than a century of ecological damage, industrial and technological expansion, and unchecked population growth has left the Earth on the brink of devastation. As the world’s governments turn inward, one man dares to envision a bolder, brighter future. That man, Reid Malenfant, has a very different solution to the problems plaguing the planet: the exploration and colonization of space. Now Malenfant gambles the very existence of time on a single desperate throw of the dice. Battling national sabotage and international outcry, as apocalyptic riots sweep the globe, he builds a spacecraft and launches it into deep space. The odds are a trillion to one against him. Or are they? “A staggering novel! If you ever thought you understood time, you’ll be quickly disillusioned when you read Manifold: Time.”—Sir Arthur C. Clarke
Download or read book Topology Now written by Robert Messer and published by American Mathematical Soc.. This book was released on 2018-10-10 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.
Download or read book Differential Manifolds written by Antoni A. Kosinski and published by Courier Corporation. This book was released on 2013-07-02 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.
Download or read book Origin written by Stephen Baxter and published by HarperCollins UK. This book was released on 2012-06-28 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2015: Astronaut Reid Malenfant is flying over the African continent, intent on examining a mysterious glowing construct in Earth’s orbit.
Download or read book Geometry of Manifolds written by and published by Academic Press. This book was released on 2011-08-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry of Manifolds
Download or read book Federal Register written by and published by . This book was released on 1989-03-20 with total page 1146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Calculus on Manifolds written by Michael Spivak and published by Westview Press. This book was released on 1965 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
Download or read book Applications of Centre Manifold Theory written by J. Carr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is presented in an informal fashion, by means of worked examples in the hope that this clarifies the use of centre manifold theory. The main application of centre manifold theory given in these notes is to dynamic bifurcation theory. Dynamic bifurcation theory is concerned with topological changes in the nature of the solutions of differential equations as para meters are varied. Such an example is the creation of periodic orbits from an equilibrium point as a parameter crosses a critical value. In certain circumstances, the application of centre manifold theory reduces the dimension of the system under investigation. In this respect the centre manifold theory plays the same role for dynamic problems as the Liapunov-Schmitt procedure plays for the analysis of static solutions. Our use of centre manifold theory in bifurcation problems follows that of Ruelle and Takens [57) and of Marsden and McCracken [51).
Download or read book Instantons and Four Manifolds written by Daniel S. Freed and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate... The book is filled with insightful remarks, proofs, and contributions that have never before appeared in print. For anyone attempting to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology, the book is a must." #Science#1 "I would strongly advise the graduate student or working mathematician who wishes to learn the analytic aspects of this subject to begin with Freed and Uhlenbeck's book." #Bulletin of the American Mathematical Society#2
Download or read book The Manifold Beauty of Genesis One written by Gregg Davidson and published by Kregel Publications. This book was released on 2021-11-16 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: See and celebrate the multilayered grandeur conveyed by the first chapter of Genesis The first chapter of the Bible's first book lays the foundation for all that follows about who God is and what God is like. Our technology-age fascination with the science of origins, however, can blind us to issues of great importance that don't address our culturally conditioned questions. Instead, Genesis One itself suggests the questions and answers that are most significant to human faith and flourishing. Geologist Gregg Davidson and theologian Ken Turner shine a spotlight on Genesis One as theologically rich literature first and foremost, exploring the layers of meaning that showcase various aspects of God's character: Song Analogy Polemic Covenant Temple Calendar Land Our very knowledge of God suffers when we fail to appreciate the Bible's ability to convey multilayered truth simultaneously. The Manifold Beauty of Genesis One offers readers the chance to cultivate an openness to Scripture's richness and a deeper faith in the Creator.
