Related papers: On a complex topological orientation for circle-eq…

A classical result in quantum topology is that oriented 2-dimensional topological quantum field theories (2-TQFTs) are fully classified by commutative Frobenius algebras. In 2006, Turaev and Turner introduced additional structure on…

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 use the geometry of the space of fields for gauged supersymmetric mechanics to construct the twisted differential equivariant K-theory of a manifold with an action by a finite group.

This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.

We use a well known problem in discrete and computational geometry (partitions of measures by $k$-fans) as a motivation and as a point of departure to illustrate many aspects, both theoretical and computational, of the problem of…

Roughly speaking, the Kakeya Conjecture asks to what extent lines which point in different directions can be packed together in a small space. In $\R^2$, the problem is relatively straightforward and was settled in the 1970s. In $\R^3$ it…

We present some results on equivariant KK-theory in the context of tensor triangular geometry. More specifically, for G a finite group, we show that the spectrum of the tensor triangulated subcategory of KK^G generated by the tensor unit…

Let $G=SU(2)$ and let $\Omega G$ denote the space of based loops in SU(2). We explicitly compute the $R(G)$-module structure of the topological equivariant $K$-theory $K_G^*(\Omega G)$ and in particular show that it is a direct product of…

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…

We express the real connective $K$ theory groups of the quaternion QL group of order $2^j\ge8$ in terms of the representation theory of by showing $ko_{4k-1}(BQL)=KSp(S^{4k+3}/\tau QL)$ where $tau$ is any fixed point free representation of…

A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.

Let $k$ be a field and let $E$ be a finite quiver. We study the structure of the finitely presented modules of finite length over the Leavitt path algebra $L_k (E)$ and show its close relationship with the finite-dimensional representations…

Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a…

KK-theory is a bivariant and homotopy-invariant functor on $C^*$-algebras that combines K-theory and K-homology. KK-groups form the morphisms in a triangulated category. Spanier-Whitehead K-Duality intertwines the homological with the…

We present several results on the geometry of the quantum projective plane CP2q. They include: explicit generators for the K-theory and the K-homology; a real calculus with a Hodge star operator; anti-selfdual connections on line bundles…

The twisted equivariant K-theory given by Freed and Moore is a K-theory which unifies twisted equivariant complex K-theory, Atiyah's `Real' K-theory, and their variants. In a general setting, we formulate this K-theory by using Fredholm…

We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on sigma-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show…

This expository paper is an introductory text on topological K-theory and the Atiyah-Singer index theorem, suitable for graduate students or advanced undegraduates already possessing a background in algebraic topology. The bulk of the…

We prove a formula for the push-forward class of Bott-Samelson resolutions in the algebraic cobordism ring of the flag bundle. We specialise our formula to connective K-theory providing a geometric interpretation to the double…

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…