Index theory studies the solutions to differential equations on geometric spaces, their
relation to the underlying geometry and topology, and applications to physics. If the space of …

We provide a homotopy theorist's point of view on $ KK $-and $ E $-theory for $ C^{*} $-
algebras. We construct stable $\infty $-categories representing these theories through a …

In this paper, we introduce the quantitative coarse Baum-Connes conjecture with coefficients
(or QCBC, for short) for proper metric spaces which refines the coarse Baum-Connes …

We introduce controlled KK-theory groups associated to a pair pA, Bq of separable C-
algebras. Roughly, these consist of elements of the usual K-theory group K0pBq that …

A quasi-representation of a group is a map from the group into a matrix algebra (or similar
object) that approximately satisfies the relations needed to be a representation. Work of …

In this paper, we study the equivariant coarse Novikov conjectures for spaces that
equivariantly and coarsely embed into admissible Hilbert-Hadamard spaces, which are a …

This is the second part of a series of papers which bridges the Chang–Weinberger–Yu
relative higher index and geometry of almost flat Hermitian vector bundles on manifolds with …

We construct a slant product/: Sp (X× Y)× K1− q (credY)→ Sp− q (X) on the analytic structure
group of Higson and Roe and the K-theory of the stable Higson corona of Emerson and …

Kasparov KK-theory for a pair of C∗-algebras (A, B) can be formulated equivalently in terms
of the K-theory of Yu's localization algebra by Dadarlat-Willett-Wu. We investigate the …

We give a proof of the Bott periodicity theorem for topological K-theory of C-algebras based
on Loring's treatment of Voiculescu's almost commuting matrices and Atiyah's rotation trick …