Lusternik-Schnirelmann category and strong category
نویسندگان
چکیده
منابع مشابه
Lusternik-Schnirelmann category of Orbifolds
The idea is to generalize to the case of orbifolds the classical Lusternik-Schnirelmann theory. This paper defines a notion of LS-category for orbifolds. We show that some of the classical estimates for the regular category have their analogue in the case of orbifolds. We examine the topic in some detail using a mixture of approaches from equivariant theory and foliations. MSC: 55M30; 57R30
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Let K be a simplicial complex and suppose that K collapses onto L. Define n to be 1 minus the minimum number of collapsible sets it takes to cover L. Then the discrete Lusternik–Schnirelmann category of K is the smallest n taken over all such L. In this paper, we give an algorithm which yields an upper bound for the discrete category. We show our algorithm is correct and give several bounds for...
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The purpose of this paper is to develop a transverse notion of Lusternik{Schnirelmann category in the eld of foliations. Our transverse category, denoted cat\j (M;F), is an invariant of the foliated homotopy type which is nite on compact manifolds. It coincides with the classical notion when the foliation is by points. We prove that for any foliated manifold catM catL cat\j (M;F), where L is a ...
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We give conditions when cat(f × g) < cat(f) + cat(g). We apply our result to show that under suitable conditions for rational maps f , mcat(f) < cat(f) is equivalent to cat(f) = cat(f×idSn). Many examples with mcat(f) < cat(f) satisfying our conditions are constructed. We also resolve one open case of Ganea’s conjecture by constructing a space X such that cat(X × S1) = cat(X) = 2. In fact for e...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1967
ISSN: 0019-2082
DOI: 10.1215/ijm/1256054563