729 research outputs found
Group actions on spheres with rank one isotropy
We show that a rank two finite group G admits a finite G-CW-complex X
homotopy equivalent to a sphere, with rank one prime power isotropy, if and
only if G does not p'-involve Qd(p) for any odd prime p. This follows from a
more general theorem which allows us to construct a finite G-CW-complex by
gluing together a given G-invariant family of representations defined on the
Sylow subgroups of G.Comment: 16 page
Quotients of
We consider closed topological 4-manifolds with universal cover
and Euler characteristic . All such manifolds
with are homotopy equivalent. In this case,
we show that there are four homeomorphism types, and propose a candidate for a
smooth example which is not homeomorphic to the geometric quotient. If
, we show that there are three
homotopy types (and between 6 and 24 homeomorphism types).Comment: 18 page
Cyclic branched coverings of Brieskorn spheres bounding acyclic 4-manifolds
We show that standard cyclic actions on Brieskorn homology 3-spheres with non-empty fixed set do not extend smoothly to any contractible smooth 4-manifold it may bound. The quotient of any such extension would be an acyclic -manifold with boundary a related Brieskorn homology sphere. We briefly discuss well known invariants of homology spheres that obstruct acyclic bounding 4-manifolds, and then use a method based on equivariant Yang-Mills moduli spaces to rule out extensions of the actions
Group actions on spheres with rank one prime power isotropy
We show that a rank two finite group G admits a finite G-CWcomplex X Sn with rank one prime power isotropy if and only if G does not p-involve Qd(p) for any odd prime p. This follows from a more general theorem which allows us to construct a finite G-CW-complex by gluing together a given G-invariant family of representations defined on the Sylow subgroups of G. © by International Press of Boston, Inc. All rights reserved
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