Product Formulae for Ozsvath-Szabo 4-manifold Invariants

Details Product Formulae for Ozsvath-Szabo 4-manifold Invariants Product Formulae for Ozsvath-Szabo 4-manifold Invariants

2007-06-03

arxiv.org/abs/0706.0339v1

Mathematics

Geometric Topology

70 pages, 2 figures

Scientific paper

We give formulae for the Ozsvath-Szabo invariants of 4-manifolds X obtained by fiber sum of two manifolds M_1, M_2 along surfaces S_1, S_2 having trivial normal bundle and genus g>0. The formulae follow from a general theorem on the Ozsvath-Szabo invariants of the result of gluing two 4-manifolds along a common boundary, which is phrased in terms of relative invariants of the pieces. These relative invariants take values in a version of Heegaard Floer homology with coefficients in modules over certain Novikov rings; the fiber sum formula follows from the theorem that this "perturbed" version of Heegaard Floer theory recovers the usual Ozsvath-Szabo invariants, when the 4-manifold in question has b^+>1. The construction allows an extension of the definition of the Ozsvath-Szabo invariants to 4-manifolds having b^+ = 1 depending on certain choices, in close analogy with Seiberg-Witten theory. The product formulae lead quickly to calculations of the Ozsvath-Szabo invariants of various 4-manifolds; in all cases the results are in accord with the conjectured equivalence between the Ozsvath-Szabo and Seiberg-Witten invariants.

Affiliated with

Also associated with

No associations

Rating

Product Formulae for Ozsvath-Szabo 4-manifold Invariants 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 Product Formulae for Ozsvath-Szabo 4-manifold Invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Product Formulae for Ozsvath-Szabo 4-manifold Invariants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-689258