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We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\K$-theory (denoted $\KH$-theory) entirely in terms of the torus pieces of open sets forming an open cover of ...
Let G=SU(2) and let \Omega G denote the space of continuous based loops in G, equipped with the pointwise conjugation action of G. It is a classical fact in topology that the ordinary cohomology H^*(\...
We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group. Moreover, we show that Walker's theorem ...
A kind of motivic stable homotopy theory of algebras is developed. Explicit fibrant replacements for the S^1-spectrum and (S^1,\G)-bispectrum of an algebra are constructed. As an application, unstable...
We show that if $A$ and $H$ are Hopf algebras that have equivalent tensor categories of comodules, then one can transport what we call a free Yetter-Drinfeld resolution of the counit of $A$ to the sam...
Abstract: In this paper, we use $\mathcal D$-split sequences and derived equivalences to provide formulas for calculation of higher algebraic $K$-groups (or mod-$p$ $K$-groups) of certain matrix subri...
Abstract: We show that contracting self-similar groups satisfy the Farrell-Jones conjectures as soon as their universal contracting cover is non-positively curved. This applies in particular to bounde...
Abstract: It is now known (or in some cases just believed) that many quantum field theories exhibit dualities, equivalences with the same or a different theory in which things appear very different, b...
Abstract: Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space ...
Abstract: Let $G$ be a compact Lie group, $H$ a closed subgroup of maximal rank and $X$ a topological $G$-space. We obtain a variety of results concerning the structure of the $H$-equivariant K-ring $...
Abstract: We introduce a construction adding low-dimensional cells to a space that satisfies certain low-dimensional conditions; it preserves high-dimensional homology with appropriate coefficients. T...
Abstract: We calculate the equivariant index formula for an infinite dimensional Clifford module canonically associated to any Riemannian manifold. It encompasses the fractional index formula of the p...
Abstract: We prove that any countable discrete and torsion free subgroup of a general linear group over an arbitrary field or a similar subgroup of an almost connected Lie group satisfies the integral...
Abstract: Let k be a field, A a unitary associative k-algebra and V a k-vector space endowed with a distinguished element 1_V. We obtain a mixed complex, simpler that the canonical one, that gives the...
Abstract: Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, we prove the local index formula for spectral triples over nonunital alg...

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