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Fundamental groups of manifolds with |
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| Authors: | J. C. Gómez-Larrañaga F. González-Acuña Wolfgang Heil |
| Affiliation: | (1) Centro de Investigación en Matemáticas, A.P. 402, Guanajuato, 36000, Gto., Mexico;(2) Instituto de Matemáticas, UNAM, Ciudad Universitaria, 04510 México, D.F., Mexico;(3) Department of Mathematics, Florida State University, Tallahasee, FL 32306, USA |
| Abstract: | A closed topological n-manifold M n is of S 1-category 2 if it can be covered by two open subsets W 1,W 2 such that the inclusions W i → M n factor homotopically through maps W i → S 1 → M n . We show that the fundamental group of such an n-manifold is a cyclic group or a free product of two cyclic groups with nontrivial amalgamation. In particular, if n = 3, the fundamental group is cyclic. |
| Keywords: | Lusternik-Schnirelmann category Coverings of n-manifolds with open S 1-contractible subsets |
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