Geodesic
ON THE RELATIVE LUSTERNIK–SCHNIRELMANN CATEGORY WITH RESPECT TO A REAL COHOMOLOGY CLASS
Glasgow mathematical journal, Tome 53 (2011) no. 1, pp. 169-183

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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]).
DOI : 10.1017/S0017089510000595
Mots-clés : Primary: 55M30, Secondary: 58E05, 37C29 
LI, TIEQIANG; SCHÜTZ, DIRK. ON THE RELATIVE LUSTERNIK–SCHNIRELMANN CATEGORY WITH RESPECT TO A REAL COHOMOLOGY CLASS. Glasgow mathematical journal, Tome 53 (2011) no. 1, pp. 169-183. doi: 10.1017/S0017089510000595
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     title = {ON {THE} {RELATIVE} {LUSTERNIK{\textendash}SCHNIRELMANN} {CATEGORY} {WITH} {RESPECT} {TO} {A} {REAL} {COHOMOLOGY} {CLASS}},
     journal = {Glasgow mathematical journal},
     pages = {169--183},
     year = {2011},
     volume = {53},
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     doi = {10.1017/S0017089510000595},
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