On the relative Lusternik-Schnirelmann category with respect to a closed 1-form

Details On the relative Lusternik-Schnirelmann category with respect to a closed 1-form On the relative Lusternik-Schnirelmann category with respect to a closed 1-form

2009-08-10

arxiv.org/abs/0908.1294v2

Mathematics

Algebraic Topology

14 pages, changed references

Scientific paper

In this article we study a homotopy invariant cat(X,B,\xi) on a pair of finite CW complexes with respect to a continuous closed 1-form. This is a generalisation of a Lusternik-Schnirelmann category developed by Farber, studying the topology of a closed 1-form. The article establishes the connection with the original notion and obtains analogous results on critical points and homoclinic cycles. We also provide a similar cuplength lower bound for cat(X,B,\xi).

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