Download or read book Torsion TQFT and Seiberg Witten Invariants of Three manifolds written by Thomas E. Mark and published by . This book was released on 2000 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Torsions of 3 dimensional Manifolds written by Vladimir Turaev and published by Birkhäuser. This book was released on 2012-12-06 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." —Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. ...Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." —Mathematical Reviews

Download or read book The Reidemeister Torsion of 3 manifolds written by Liviu I. Nicolaescu and published by Walter de Gruyter. This book was released on 2003 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work discusses the theoretical foundations of torsion, one of the oldest topological variants. It presents the work of Reidmeister, Taubes, Turaev and the author, focusing particularly on diverse examples and techniques rather than abstract generalizations.

Download or read book Seiberg Witten Invariants of 4 manifolds with Circle Actions written by Scott Jeremy Baldridge and published by . This book was released on 2001 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Wild World of 4 Manifolds written by Alexandru Scorpan and published by American Mathematical Society. This book was released on 2022-01-26 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. —MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. — Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold—the intersection form—and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.

Download or read book Seiberg Witten Invariants on 3 manifolds with an Orientation Reversing Involution written by Jaewon Lee and published by . This book was released on 2009 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is devoted to the study of Seiberg-Witten theory for three dimensional manifolds in the presence of involutions. G. Tian and S. Wang explored real Seiberg-Witten invariants under the real structure of a Kahler manifold, which is conjugate linear in a proper sense. Their real structure, however, does not preserve spinc structure. a three-dimensional manifold, there is no such real structure. However, an orientation reversing involution on a three-dimensional spin manifold gives the powerful technique, like the real structure from G. Tian and S. Wang. Inspired by D. Freed, we know that if an orientation reversing involution preserves a pin structure, there always exists a self-adjoint lifting on complex spinor bundle satisfying certain conditions. We call the extension of lifting on spinc structure to a real structure on a three-dimensional spin manifold. My thesis is centered around the issues of Seiberg-Witten equations, the dimension and the orientability of the equivariant Seiberg-Witten moduli space with a real structure in our sense. Moreover, integer valued equivariant Seiberg-Witten invariants can be defined on a three-dimensional manifold with a dividing fixed point set.

Download or read book The Seiberg Witten Equations and Applications to the Topology of Smooth Four manifolds written by John W. Morgan and published by Princeton University Press. This book was released on 1996 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.

Download or read book Floer Homology Gauge Theory and Low Dimensional Topology written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2006 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2000 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Seiberg Witten and Gromov Invariants for Symplectic 4 manifolds written by Clifford Taubes and published by . This book was released on 2005 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: On March 28-30, 1996, International Press, the National Science Foundation, and the University of California sponsored the First Annual International Press Lecture Series, held on the Irvine campus. This volume consists of four papers comprising the proof of the author's result relating the Seiberg-Witten and Gromov invariants of four manifolds.

Download or read book Invariants of Knots and 3 manifolds Kyoto 2001 written by Tomotada Ohtsuki and published by . This book was released on 2002 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry Topology written by and published by . This book was released on 2008 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully refereed international journal dealing with all aspects of geometry and topology and their applications.

Download or read book Bordered Heegaard Floer Homology written by Robert Lipshitz and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ^HF of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ^HF. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1770 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Seiberg Witten Theory of Homology 3 spheres written by Weimin Chen (University and college faculty member) and published by . This book was released on 1998 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Torsion Invariants of 3 orbifolds Equivariant Corks Heegaard Floer Homology written by Biji Wong and published by . This book was released on 2017 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is comprised of two parts. In the first part, we construct a combinatorial invariant of 3-orbifolds with singular set a link that generalizes the Turaev torsion invariant of 3-manifolds. We give several gluing formulas from which we derive two consequences. the first is an understanding of how the components of the invariant change when we remove a curve from the singular set. The second is a formula relating the invariant of the 3-orbifold to the Turaev torsion invariant of the underlying 3-manifold in the case when the singular set is a nullhomologous knot. In the second part, we use the Heegaard Floer techniques in [3] to show that for any finite subgroup G of SO(4) there exists a contractible smooth 4 manifold with an effective G-action on its boundary so that the twists associated to the non-trivial elements of G don't extend to diffeomorphisms of the entire manifold.

Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.