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math.AT2008★ 1 cited
Small values of the Lusternik-Schnirelmann category for manifolds
Alexander N. Dranishnikov, Mikhail G. Katz, Yuli B. Rudyak
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by gen…
math.GR2008
Mapping class groups have finite asymptotic dimension
Gregory C. Bell, Alexander Dranishnikov
By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.