Bordered Heegaard Floer homology: Invariance and pairing

Details Bordered Heegaard Floer homology: Invariance and pairing Bordered Heegaard Floer homology: Invariance and pairing

2008-10-03

arxiv.org/abs/0810.0687v4

Mathematics

Geometric Topology

175 pages, 57 figures; v4: Substantial revisions, added index, glossary of notation, flip book

Scientific paper

We 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-infinity module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A-infinity 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, we 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^. We relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

Affiliated with

Also associated with

No associations

Rating

Bordered Heegaard Floer homology: Invariance and pairing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bordered Heegaard Floer homology: Invariance and pairing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bordered Heegaard Floer homology: Invariance and pairing will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-410209