Related papers: Homotopy-theoretic E-theory and n-order

Let $X$ be a finite CW complex and let $h_1, h_2: C(X)\to A$ be two unital \hm s, where $A$ is a unital C*-algebra. We study the problem when $h_1$ and $h_2$ are approximately homotopic. We present a $K$-theoretical necessary and sufficient…

Hyperoctahedral homology for involutive algebras is the homology theory associated to the hyperoctahedral crossed simplicial group. It is related to equivariant stable homotopy theory via the homology of equivariant infinite loop spaces. In…

The aim of this paper is to show that the most elementary homotopy theory of $\mathbf{G}$-spaces is equivalent to a homotopy theory of simplicial sets over $\mathbf{BG}$, where $\mathbf{G}$ is a fixed group. Both homotopy theories are…

We introduce certain $C^*$-algebras and $k$-graphs associated to $k$ finite dimensional unitary representations $\rho_1,...,\rho_k$ of a compact group $G$. We define a higher rank Doplicher-Roberts algebra $\mathcal{O}_{\rho_1,...,\rho_k}$,…

The multipullback quantization of complex projective spaces lacks the naive quantum CW-complex structure because the quantization of an embedding of the $n$-skeleton into the $(n+1)$-skeleton does not exist. To overcome this difficulty, we…

We define united KK-theory for real C*-algebras A and B such that A is separable and B is sigma-unital, extending united K-theory in the sense that KK\crt(\R, B) = K\crt(B). United KK-theory contains real, complex, and self-conjugate…

This dissertation comprises three collections of results, all united by a common theme. The theme is the study of categories via algebraic techniques, considering categories themselves as algebraic objects. This algebraic approach to…

We construct a Spanier-Whitehead type duality functor relating finite $\mathcal{C}$-spectra to finite $\mathcal{C}^{\mathrm{op}}$-spectra and prove that every $\mathcal{C}$-homology theory is given by taking the homotopy groups of a…

We establish model category structures on algebras and modules over operads in symmetric spectra, and study when a morphism of operads induces a Quillen equivalence between corresponding categories of algebras (resp. modules) over operads.

We consider modules E over a C*-algebra A which are equipped with a map into A_+ that has the formal properties of a norm. We completely determine the structure of these modules. In particular, we show that if A has no nonzero commutative…

The purpose of this paper is to generalise Sullivan's rational homotopy theory to non-nilpotent spaces, providing an alternative approach to defining Toen's schematic homotopy types over any field k of characteristic zero. New features…

We study natural subalgebras Ch_E(G) of group cohomology defined in terms of infinite loop spaces E and give representation theoretic descriptions of those based on QS^0 and the Johnson-Wilson theories E(n). We describe the subalgebras…

Connectivity is a homotopy invariant property of separable C*-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C*-algebras using…

This paper begins with an exposition of the author's research on the category of BP_*BP-comodules, much of which is joint with Neil Strickland. The main result of that work is that the category of E(n)_*E(n)-comodules is equivalent to a…

Using methods developed by Franke, we obtain algebraic classification results for modules over certain symmetric ring spectra ($S$-algebras). In particular, for any symmetric ring spectrum $R$ whose graded homotopy ring $\pi_*R$ has graded…

The homotopy symmetric $C^*$-algebras are those separable $C^*$-algebras for which one can unsuspend in E-theory. We find a new simple condition that characterizes homotopy symmetric nuclear $C^*$-algebras and use it to show that the…

We show that the categories of compact Lie groups and complex reductive groups (not necessarily connected) are homotopy equivalent topological categories. In other words, the corresponding categories enriched in the homotopy category of…

The bootstrap programme for finding exact S-matrices of integrable quantum field theories with N=1 supersymmetry is investigated. New solutions are found which have the same fusing data as bosonic theories related to the classical affine…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

We provide the rigorous foundations for a categorical approach to the classification of C*-dynamics up to cocycle conjugacy. Given a locally compact group $G$, we consider a category of (twisted) $G$-C*-algebras, where morphisms between two…