Related papers: The period-index problem for twisted topological K…
Let $A$ be a ring equipped with a derivation $\delta $. We study differential Azumaya $A$ algebras, that is, Azumaya $A$ algebras equipped with a derivation that extends $\delta $. We calculate the differential automorphism group of the…
Existence and spatio-temporal patterns of periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer $O(2) \times \Gamma \times \mathbb Z_2$-equivariant degree theory,…
We prove that Toen's secondary Grothendieck ring is isomorphic to the Grothendieck ring of smooth proper pretriangulated dg categories previously introduced by Bondal, Larsen and Lunts. Along the way, we show that those short exact…
We extend the result of Blumberg and Mandell on K-theoretic Tate-Poitou duality at odd primes which serves as a spectral refinement of the classical arithmetic Tate-Poitou duality. The duality is formulated for the $K(1)$-localized…
By applying the idea of viewing the octonions as an associative algebra in certain tensor categories, or more precisely as a twisted group algebra by a 2-cochain, we show that the octonions form an Azumaya algebra in some suitable braided…
Recently it has been shown that D-branes in orientifolds are not always described by equivariant Real K-theory. In this paper we define a previously unstudied twisted version of equivariant Real K-theory which gives the D-brane spectrum for…
We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be…
Twisted complex $K$-theory can be defined for a space $X$ equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of $H^3(X;\Z)$. We…
This paper presents, by example, an index theory appropriate to algebras without trace. Whilst we work exclusively with the Cuntz algebras the exposition is designed to indicate how to develop a general theory. Our main result is an index…
We study the C*-closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact connected manifold X with non-empty boundary. We find short exact sequences in K-theory…
Generalizing a theorem of Albert, Saltman showed that an Azumaya algebra $A$ over a ring represents a $2$-torsion class in the Brauer group if and only if there is an algebra $A'$ in the Brauer class of $A$ admitting an involution of the…
We establish a 6-term left exact sequence, involving Galois cohomology of the base field $\mathbb K$, and the Brauer-Picard groupoid of a fusion category. This generalizes a result of Etingof, Nikshych, and Ostrik to the setting where…
The Oka principle is a heuristic in complex geometry which states that, for a wide class of complex-analytic problems concerning Stein spaces, any obstruction to finding a holomorphic solution is purely topological. A classical theorem of…
A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…
The duality between $E_8\times E_8$ heteritic string on manifold $K3\times T^2$ and Type IIA string compactified on a Calabi-Yau manifold induces a correspondence between vector bundles on $K3\times T^2$ and Calabi-Yau manifolds. Vector…
We provide easily-verified necessary and sufficient conditions for a skew group ring, or more generally, a crossed product ring, to be an Azumaya algebra. We use our results to show that (suitable localisations of) skew group rings…
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
Let $M$ be a compact manifold. and $D$ a Dirac type differential operator on $M$. Let $A$ be a $C^*$-algebra. Given a bundle $W$ of $A$-modules over $M$ (with connection), the operator $D$ can be twisted with this bundle. One can then use a…
Using methods from algebraic topology and group cohomology, I pursue Grothendieck's question on equality of geometric and cohomological Brauer groups in the context of complex-analytic spaces. The main result is that equality holds under…
B-fields over a groupoid with involution are defined as Real graded Dixmier-Douady bundles. We use these to introduce the Real graded Brauer group which constitutes the set of twistings for Atiyah's KR-functor in the category of locally…