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ON THE RELATIVE LUSTERNIK–SCHNIRELMANN CATEGORY WITH RESPECT TO A REAL COHOMOLOGY CLASS

Published online by Cambridge University Press:  25 August 2010

TIEQIANG LI  and
DIRK SCHÜTZ
TIEQIANG LI
Affiliation:
Department of Mathematical Sciences, Durham University, South Road, Durham DH1 3LE, UK e-mail: tieqiang.li@durham.ac.uk, dirk.schuetz@durham.ac.uk
DIRK SCHÜTZ
Affiliation:
Department of Mathematical Sciences, Durham University, South Road, Durham DH1 3LE, UK e-mail: tieqiang.li@durham.ac.uk, dirk.schuetz@durham.ac.uk
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Abstract

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In this paper, we study a homotopy invariant cat(X, B, [ω]) on a pair (X, B) of finite CW complexes with respect to the cohomology class of a continuous closed 1-form ω. This is a generalisation of a Lusternik–Schnirelmann-category-type cat(X, [ω]), developed by Farber in [3, 4], studying the topology of a closed 1-form. This paper establishes the connection with the original notion cat(X, [ω]) and obtains analogous results on critical points and homoclinic cycles. We also provide a similar ‘cuplength’ lower bound for cat(X, B, [ω]).

Keywords

Primary: 55M30Secondary: 58E0537C29
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 1 , January 2011 , pp. 169 - 183
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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