Symmetry groups of non-simply-connected four-manifolds

Details Symmetry groups of non-simply-connected four-manifolds Symmetry groups of non-simply-connected four-manifolds

2007-07-25

arxiv.org/abs/0707.3835v1

Mathematics

Geometric Topology

15 pages

Scientific paper

Let M be a closed, connected, orientable topological four-manifold with $H_1(M)$ nontrivial and free abelian, $b_2(M)\ne 0, 2$, and $\chi(M)\ne 0$. Then the only finite groups which admit homologically trivial, locally linear, effective actions on M are cyclic. The proof uses equivariant cohomology, localization, and a careful study of the first cohomology groups of the (potential) singular set.

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