arXiv subjects

Michael P. McCooey

Publications and source records attributed to Michael P. McCooey.

3 recordsLinked to original sources

arXiv2007

Groups that act pseudofreely on S^2 x S^2

Recall that a pseudofree group action on a space is one whose singular set consists only of isolated points. In this paper, we classify all of the finite groups which admit pseudofree actions on S^2 x S^2. The groups turn out to be exactly the expected ones: those which admit orthogonal pseudofree actions on S^2 x S^2 as a subset of R^3 x R^3. They are explicitly listed. This paper can be viewed as a companion to a paper of Edmonds, math.GT/9809055.

math.GT↗

arXiv2000

Four-Manifolds which admit Z_p x Z_p actions

We show that the simply-connected four-manifolds which admit locally linear, homologically trivial actions by rank two finite abelian groups are homeomorphic to connected sums of CP^2, -CP^2, and S^2 x S^2 (with one exception: pseudofree Z_3 x Z_3 actions on the Chern manifold), and also establish an equivariant decompostion theorem. This generalizes results from a 1970 paper by Orlik and Raymond, and complements more recent work of Fintushel, Yoshida, and Huck on S^1 actions. In each case, the simply-connected four-manifolds which support such actions are essentially the same.

math.GT↗

arXiv2000

Symmetry groups of four-manifolds

If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply-connected four-manifold with second Betti number at least three, then it must be isomorphic to a subgroup of S^1 x S^1, and the action must have nonempty fixed-point set. Our results strengthen and complement recent work by Edmonds, Hambleton and Lee, and Wilczynski, among others. Our tools include representation theory, finite group theory, and Borel equivariant cohomology.

math.GT↗