Bordered Heegaard Floer Homology

Released on by Robert Lipshitz
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  • Bordered Heegaard Floer Homology Book Detail

  • Author : Robert Lipshitz
  • Release Date : 2018-08-09
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 294
  • ISBN 13 : 1470428881
  • File Size : 42,42 MB
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Bordered Heegaard Floer Homology by Robert Lipshitz PDF Summary

Book Description: 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.

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Bordered Heegaard Floer Homology

Bordered Heegaard Floer Homology

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The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a different

Cornered Heegaard Floer Homology

Cornered Heegaard Floer Homology

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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, ca