Bordered Heegaard Floer Homology, Satellites, and Decategorification
Author: Tsvetelina Vaneva Petkova
Publisher:
Published: 2012
Total Pages:
ISBN-13:
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Author: Tsvetelina Vaneva Petkova
Publisher:
Published: 2012
Total Pages:
ISBN-13:
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: 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: Tova Helen Fell Brown
Publisher:
Published: 2011
Total Pages: 55
ISBN-13:
DOWNLOAD EBOOKThe 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: Jonathan Hanselman
Publisher:
Published: 2014
Total Pages:
ISBN-13:
DOWNLOAD EBOOKWe 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: Daniel Selahi Durusoy
Publisher:
Published: 2008
Total Pages: 104
ISBN-13:
DOWNLOAD EBOOKAuthor: András Juhász
Publisher:
Published: 2021
Total Pages: 186
ISBN-13: 9781470468057
DOWNLOAD EBOOKAuthor: Faramarz Vafaee
Publisher:
Published: 2014
Total Pages: 65
ISBN-13: 9781321119053
DOWNLOAD EBOOKAuthor: Sridhar Rajagopalan
Publisher:
Published: 2007
Total Pages: 80
ISBN-13:
DOWNLOAD EBOOKAuthor: Arno Wildi
Publisher:
Published: 2021
Total Pages: 0
ISBN-13:
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