We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. If the fibers of G → B are simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result being given by an Atiyah-Singer type formula. We also study traces on the corresponding algebras of pseudodifferentia...

We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.

We describe an effective algorithm for computing Seiberg-Witten invariants of lens spaces. We apply it to two problems: (i) to compute the Froyshov invariants of a large family of lens spaces; (ii) to show that the knowledge of the Seiberg-Witten invariants of a lens space is topologically equivalent to the knowledge of its Casson-Walker invariant and of its MilnorTuraev torsion. Problem (i) ha...

Recently Anishetty, Majumdar and Sharatchandra have proposed a way of characterizing topologically non-trivial configurations for 2+1-dimensional Yang-Mills theory in a local and manifestly gauge invariant manner. In this paper we develop criteria to locate such objects in lattice gauge theory and find them in numerical simulations. PACS No.(s) 11.15 Ha, 11.15 Tk Typeset using REVTEX Present ad...

A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly realcompact. Our proof of this result is based on a thorough study of the interaction between the ...

We study the action of the mapping class groupMod(S) on the boundary ∂Q of quasifuchsian space Q. Among other results, Mod(S) is shown to be topologically transitive on the subset C ⊂ ∂Q of manifolds without a conformally compact end. We also prove that any open subset of the character varietyX (π1(S),PSL2 C) intersecting ∂Q does not admit a nonconstant Mod(S)-invariant meromorphic function. Th...

We will extend the topological Gromov-Hausdorff stability [ 2 ] from homeomorphisms to finitely generated actions. prove that if an action is expansive and has shadowing property, then it topologically GH-stable. From this we derive examples of GH-stable actions discrete Heisenberg group on tori. Finally, GH-stability invariant under isometric conjugacy.

There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are assigned topologically are naturally invariant under spatial expansion, supporting a continuous reduction in density towards zero, unless additional cohesive int...

We introduce a relative Gurevich pressure for random countable topologically mixing Markov shifts. It is shown that the relative variational principle holds for this notion of pressure. We also prove a relative RuellePerron-Frobenius theorem which enables us to construct a wealth of invariant Gibbs measures for locally fiber Hölder continuous functions. This is accomplished via a new constructi...

We show that one dimensional maps f with strictly positive Lyapunov exponents almost everywhere admit an absolutely continuous invariant measure. If f is topologically transitive some power of f is mixing and in particular the correlation of Hölder continuous observables decays to zero. The main objective of this paper is to show that the rate of decay of correlations is determined, in some sit...