Related papers: Twisted entire cyclic cohomology, J-L-O cocycles a…

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite CW-complexes with equivariant stable projective…

We generalize quantum Drinfeld Hecke algebras by incorporating a 2-cocycle on the associated finite group. We identify these algebras as specializations of deformations of twisted skew group algebras, giving an explicit connection to…

We propose a general procedure to construct noncommutative deformations of an algebraic submanifold $M$ of $\mathbb{R}^n$, specializing the procedure [G. Fiore, T. Weber, Twisted submanifolds of $\mathbb{R}^n$, arXiv:2003.03854] valid for…

We develop a theory of ``ad hoc'' Chern characters for twisted matrix factorizations associated to a scheme $X$, a line bundle ${\mathcal L}$, and a regular global section $W \in \Gamma(X, {\mathcal L})$. As an application, we establish the…

We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients…

For $G$ a finite group, a normalized 2-cocycle $\alpha\in Z^{2}\big(G,{\mathbb S}^{1}\big)$ and $X$ a $G$-space on which a normal subgroup $A$ acts trivially, we show that the $\alpha$-twisted $G$-equivariant $K$-theory of $X$ decomposes as…

We propose Weil and Cartan models for the equivariant cohomology of noncommutative spaces which carry a covariant action of Drinfel'd twisted symmetries. The construction is suggested by the noncommutative Weil algebra of Alekseev and…

The Jaffe-Lesniewski-Osterwalder (JLO) character is a homomorphism from K-homology to entire cyclic cohomology. This paper extends the domain of the JLO character to include Type II noncommutative geometry, the geometry represented by…

Notes for some talks given at the seminar on characteristic classes at NTNU in autumn 2006. In the paper a proof of the existence of a Chern-character from complex K-theory to any cohomology theory with values in graded Q-algebras is given.…

Let $q=|q|e^{i\pi\theta},\,\theta\in(-1,1],$ be a nonzero complex number such that $|q|\neq 1$ and consider the compact quantum group $U_q(2)$. For $\theta\notin\mathbb{Q}\setminus\{0,1\}$, we obtain the $K$-theory of the $C^*$-algebra…

An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of…

Starting with a $\mathbb{C}^*$-valued cocycle on the global quotient orbifold $X // G$, we apply transgression techniques for 2-gerbes, as developed by Lupercio and Uribe, to construct a gerbe on the orbifold loop space $\mathcal{L}(X//G)$.…

The symmetry-resolved Krylov complexity is a useful tool in studying chaotic properties of systems that are endowed with symmetries. We investigate the conditions under which an invariant operator would have the symmetry-resolved Krylov…

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an…

We show how a suitably twisted Spin-cobordism spectrum connects to the question of existence of metrics of positive scalar curvature on closed, smooth manifolds by building on fundamental work of Gromov, Lawson, Rosenberg, Stolz and others.…

We discuss the notion of a q-PD-envelope considered by Bhatt and Scholze in their recent theory of q-crystalline cohomology and explain the relation with our notion of a divided polynomial twisted algebra. Together with an interpretation of…

We sketch a quick and dirty geometric approach to the Tate-Swan cohomology of equivariant spectra, illustrating it with conjectural applications to Atiyah-Segal $K$-theory of circle actions, and a possible geometric model for the…

We present an intelligible review of recent results concerning cyclic cocycles in the spectral action and one-loop quantization. We show that the spectral action, when perturbed by a gauge potential, can be written as a series of…

Kitchloo and Morava give a strikingly simple picture of elliptic cohomology at the Tate curve by studying a completed version of $S^1$-equivariant $K$-theory for spaces. Several authors (cf [ABG],[KM],[L]) have suggested that an equivariant…

In this thesis we study field theories written on a particular model of noncommutative spacetime, the Groenewold-Moyal (GM) plane. We start with briefly reviewing the novel features of field theories on GM plane e.g. the $\ast$-product,…