Bordered Heegaard Floer Homology

Author : Robert Lipshitz
Publisher : American Mathematical Soc.
ISBN 13 : 1470428881
Total Pages : 279 pages
Book Rating : 4.84/5 ( download)

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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 279 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.

Author : Robert Lipshitz
Publisher :
ISBN 13 : 9781470447489
Total Pages : 279 pages
Book Rating : 4.87/5 ( download)

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Download or read book Bordered Heegaard Floer Homology written by Robert Lipshitz and published by . This book was released on 2018 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Thomas Henry Hockenhull
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.71/5 ( download)

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Download or read book The Bordered Heegaard Floer Homology of Link Complements written by Thomas Henry Hockenhull and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Tsvetelina Vaneva Petkova
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.25/5 ( download)

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Download or read book Bordered Heegaard Floer Homology, Satellites, and Decategorification written by Tsvetelina Vaneva Petkova and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Christopher L Douglas
Publisher : American Mathematical Soc.
ISBN 13 : 1470437716
Total Pages : 111 pages
Book Rating : 4.18/5 ( download)

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Download or read book Cornered Heegaard Floer Homology written by Christopher L Douglas and published by American Mathematical Soc.. This book was released on 2020-02-13 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. The authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.

Author : Jonathan Hanselman
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.06/5 ( download)

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Download or read book Bordered Heegaard Floer Homology and Graph Manifolds written by Jonathan Hanselman and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We use the techniques of bordered Heegaard Floer homology to investigate the Heegaard Floer homology of graph manifolds. Bordered Heegaard Floer homology allows us to split a graph manifold into pieces and perform computations for each piece separately. The resulting invariants can then be combined by a simple algebraic procedure to recover HFhat. Graph manifolds by definition decompose into pieces which are S1-bundles over surfaces. This decomposition makes them particularly well suited to the divide-and-conquer techniques of bordered Heegaard Floer homology. In fact, the problem reduces to computing bordered Heegaard Floer invariants of just two pieces. The first invariant is the type D trimodule associated to the trivial S1-bundle over the pair of pants.

Author : Frédéric Bourgeois
Publisher : Springer Science & Business Media
ISBN 13 : 3319020366
Total Pages : 538 pages
Book Rating : 4.65/5 ( download)

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Download or read book Contact and Symplectic Topology written by Frédéric Bourgeois and published by Springer Science & Business Media. This book was released on 2014-03-10 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

Author : Jan de Gier
Publisher : Springer Nature
ISBN 13 : 3030624978
Total Pages : 798 pages
Book Rating : 4.72/5 ( download)

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Download or read book 2019-20 MATRIX Annals written by Jan de Gier and published by Springer Nature. This book was released on 2021-02-10 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

Author : Tova Helen Fell Brown
Publisher :
ISBN 13 :
Total Pages : 55 pages
Book Rating : 4.14/5 ( download)

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Download or read book Bordered Heegaard Floer Homology and Four-manifolds with Corners written by Tova Helen Fell Brown and published by . This book was released on 2011 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Heegaard Floer hat invariant is defined on closed 3-manifolds, with a related invariant for 4-dimensional cobordisms, forming a 3+1 topological quantum field theory. Bordered Heegaard Floer homology generalizes this invariant to parametrized Riemann surfaces and to cobordisms between them, yielding a 2+1 TQFT. We discuss an approach to synthesizing these two theories to form a 2+1+1 TQFT, by defining Heegaard Floer invariants for Lefschetz fibrations with corners.

Author : Peter S. Ozsváth
Publisher : American Mathematical Soc.
ISBN 13 : 1470417375
Total Pages : 423 pages
Book Rating : 4.76/5 ( download)

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Download or read book Grid Homology for Knots and Links written by Peter S. Ozsváth and published by American Mathematical Soc.. This book was released on 2015-12-04 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.