92,056 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
Shock capturing
Recent developments which have improved the understanding of how finite difference methods resolve discontinuous solutions to hyperbolic partial differential equations are discussed. As a result of this understanding improved shock capturing methods are currently being developed and tested. Some of these methods are described and numerical results are presented showing their performance on problems containing shocks in one and two dimensions. A conservative difference scheme is defined. Conservation implies that, except in very special circumstances, shocks must be spread over at least two grid intervals. These two interval shocks are actually attained in one dimension if the shock is steady and an upwind scheme is used. By analyzing this case, the reason for this excellent shock resolution can be determined. This result is used to provide a mechanism for improving the resolution of two dimensional steady shocks. Unfortunately, this same analysis shows that these results cannot be extended to shocks which move relative to the computing grid. Total variation diminishing (TVD) finite difference schemes and flux limiters are introduced to deal with money shocks and contact discontinuities
TVD finite difference schemes and artificial viscosity
The total variation diminishing (TVD) finite difference scheme can be interpreted as a Lax-Wendroff scheme plus an upwind weighted artificial dissipation term. If a particular flux limiter is chosen and the requirement for upwind weighting is removed, an artificial dissipation term which is based on the theory of TVD schemes is obtained which does not contain any problem dependent parameters and which can be added to existing MacCormack method codes. Numerical experiments to examine the performance of this new method are discussed
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
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