Aniruddha C. Naolekar

Chaotic group actions on manifolds

Abstract We construct chaotic actions of certain finitely generated infinite abelian groups on even-dimensional spheres, and of finite index subgroups of SL n ( Z ) on tori. We also study chaotic group actions via compactly supported homeomorphisms on open manifolds.

Note on the characteristic rank of vector bundles

We define the notion of characteristic rank, charrankX(ξ), of a real vector bundle ξ over a connected finite CW-complex X. This is a bundle-dependent version of the notion of characteristic rank introduced by Július Korbaš in 2010. We obtain bounds for the cup length of manifolds in terms of the characteristic rank of vector bundles generalizing a theorem of Korbaš and compute the characteristic rank of vector bundles over the Dold manifolds, the Moore spaces and the stunted projective spaces amongst others.

An axiomatic approach to equivariant cohomology theories

This paper presents a translation of a theorem of Cartan into an equivariant setting. This work is largely based on the study of the homotopical algebra in the sense of Quillen of the category of simplicial objects over the category of rationalOg-vector spaces. The application is a solution to the equivariant commutative cochain problem. This solution is slightly better than the solution obtained earlier by Triantafillou in that the transformation groupG need not be finite.

REALIZING COHOMOLOGY CLASSES AS EULER CLASSES

For a space X, let Ek(X), Eks(X) and Ek○ (X) denote respectively the set of Euler classes of oriented k-plane bundles over X, the set of Euler classes of stably trivial k-plane bundles over X and the spherical classes in Hk(X; ℤ). We prove some general facts about the sets Ek(X), Eks(X) and Ek○ (X). We also compute these sets in the cases where X is a projective space, the Dold manifold P(m, 1) and obtain partial computations in the case that X is a product of spheres.

Characteristic rank of vector bundles over Stiefel manifolds

The characteristic rank of a vector bundle ξ over a finite connected CW-complex X is by definition the largest integer

Euler classes of vector bundles over iterated suspensions of real projective spaces

{k, 0 \leq k \leq \mathrm{dim}(X)}

ON THE NOTION OF RESIDUAL FINITENESS FOR G-SPACES

, such that every cohomology class