Every compact manifold carries a completely hyperbolic diffeomorphism

A diffeomorphism anomaly in every dimension

Field-theoretic pure gravitational anomalies only exist in 4k+2 dimensions. However, canonical quantization of non-field-theoretic systems may give rise to diffeomorphism anomalies in any number of dimensions. I present a simple example, where a higher-dimensional generalization of the Virasoro algebra arises upon quantization. The Polyakov action in string theory is nothing but 1+1-dimensional...

A Hyperbolic 4-Manifold

There is a regular 4-dimensional polyhedron with 120 dodecahedra as 3-dimensional faces. (Coxeter calls it the "120-cell".) The group of symmetries of this polyhedron is the Coxeter group with diagram: For each pair of opposite 3-dimensional faces of this polyhedron there is a unique reflection in its symmetry group which interchanges them. The result of identifying opposite faces by these refl...

Completely Reducible p-compact Groups

Rational automorphisms of products of simple p-compact groups are shown to be composites of products of rational automorphisms of the individual factors and permutation maps.

On images of continuous functions from a compact manifold to Euclidean space

A Fake Compact Contractible 4-manifold

Here we construct a fake smooth structure on a compact contractible 4-manifold W , where W is a well-known Mazur manifold obtained by attaching in two-handle to S x B along its boundary as in Figure 1. * Here we use the conventions of [2]. The results of this paper imply: Theorem 1. There is a smooth contractible 4-manifold V with dV = d W, such that V is homeomorphic but not diffeomorphic to W...