8,127 research outputs found
Any finite group acts freely and homologically trivially on a product of spheres
The main theorem is that if K is a finite CW complex with finite fundamental
group G and universal cover homotopy equivalent to a product of spheres X, then
G acts smoothly and freely on X x S^n for any n greater than or equal to the
dimension of X. If the G-action on the universal cover of K is homologically
trivial then so is the action on X x S^n.
Unlu and Yalcin recently showed that for every finite group G, there is a
finite CW complex K with fundamental group G which acts homologicially
trivially on the universal cover of K.
Thus every finite group acts smoothly, freely, and homologically trivially on
a product of spheres.Comment: 11 pages. Final version. To appear in the Proceedings of the American
Mathematical Societ
A two component link with Alexander polynomial one is concordant to the Hopf link
Four-dimensional surgery is used to show that a two component link with
Alexander polynomial one is topologically concordant to the Hopf link.Comment: To appear in the Mathematical Proceedings of the Cambridge
Philosophicial Societ
The topological K-theory of certain crystallographic groups
Let Gamma be a semidirect product of the form Z^n rtimes Z/p where p is prime
and the Z/p-action on Z^n is free away from the origin. We will compute the
topological K-theory of the real and complex group C*-algebra of Gamma and show
that Gamma satisfies the unstable Gromov-Lawson-Rosenberg Conjecture. On the
way we will analyze the (co-)homology and the topological K-theory of the
classifying spaces BGamma and underbar{B}Gamma. The latter is the quotient of
the induced Z/p-action on the torus T^n.Comment: 46 pages. Final version. Accepted for publication in the Journal of
Noncommutative Geometr
There is no tame triangulation of the infinite real Grassmannian
We show that there is no triangulation of the infinite real Grassmannian of
k-planes in R^\infty which is nicely situated with respect to the coordinate
axes. In terms of matroid theory, this says there is no triangulation of the
Grassmannian subdividing the matroid stratification. This is proved by an
argument in projective geometry, considering a specific sequence of
configurations of points in the plane.Comment: 11 page
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