On the classification of Floer-type theories

Details On the classification of Floer-type theories On the classification of Floer-type theories

2007-04-10

arxiv.org/abs/0704.1330v1

Mathematics

Geometric Topology

30 pages

Scientific paper

In this paper we outline a program for the classification of Floer-type theories, (or defining invariants of finite type for families). We consider Khovanov complexes as a local system on the space of knots introduced by V. Vassiliev and construct the wall-crossing morphism. We extend this system to the singular locus by the cone of this morphism and introduce the definition of the local system of finite type. This program can be further generalized to the manifolds of dimension 3 and 4.

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