Heegaard Floer Homology for Webs
Author: Arno Wildi
Publisher:
Published: 2021
Total Pages: 0
ISBN-13:
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Author: Arno Wildi
Publisher:
Published: 2021
Total Pages: 0
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DOWNLOAD EBOOKAuthor: Robert Lipshitz
Publisher: American Mathematical Soc.
Published: 2018-08-09
Total Pages: 294
ISBN-13: 1470428881
DOWNLOAD EBOOKThe 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: Peter S. Ozsváth
Publisher: American Mathematical Soc.
Published: 2015-12-04
Total Pages: 423
ISBN-13: 1470417375
DOWNLOAD EBOOKKnot 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.
Author: Raif Rustamov
Publisher:
Published: 2005
Total Pages: 142
ISBN-13:
DOWNLOAD EBOOKAuthor: Adam Simon Levine
Publisher:
Published: 2010
Total Pages: 264
ISBN-13:
DOWNLOAD EBOOKAuthor: Lawrence Pierce Roberts
Publisher:
Published: 2004
Total Pages: 484
ISBN-13:
DOWNLOAD EBOOKAuthor: Christopher L Douglas
Publisher: American Mathematical Soc.
Published: 2020-02-13
Total Pages: 111
ISBN-13: 1470437716
DOWNLOAD EBOOKBordered 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: Sridhar Rajagopalan
Publisher:
Published: 2007
Total Pages: 80
ISBN-13:
DOWNLOAD EBOOKAuthor: Marco Marengon
Publisher:
Published: 2017
Total Pages:
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DOWNLOAD EBOOKAuthor: Tsvetelina Vaneva Petkova
Publisher:
Published: 2012
Total Pages:
ISBN-13:
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