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The Lusternik–Schnirelmann category and the fundamental group
The Lusternik-Schnirelmann category and the fundamental group ALEXANDER DRANISHNIKOVWe prove that cat LS X Ä cd. 1 .X // C dim X 1 2 for every CW-complex X where cd. 1 .X // denotes the cohomological dimension of the fundamental group of X .