Related papers: Twisted differential cohomology
In this paper it is shown that multiplicative cohomology theories that are rationally even -- a technical condition that is often satisfied -- the Hopkins-Singer construction of generalized differential cohomology has a unital, graded…
This is an expository account of the following result: we can construct a group by means of twisted Z_2-graded vectorial bundles which is isomorphic to K-theory twisted by any degree three integral cohomology class.
This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion…
Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd…
In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of…
In this paper, we develop twisted $K$-theory for stacks, where the twisted class is given by an $S^1$-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure $K^i_\alpha…
Twisted K-theory has its origins in the author's PhD thesis [27] : http://www.numdam.org/item?id=ASENS_1968_4_1_2_161_0 and in the paper with P. Donovan http://www.numdam.org/item?id=PMIHES_1970__38__5_0 The objective of this paper is to…
This article is a survey on the cohomology of a reductive algebraic group with coefficients in twisted representations. A large part of the paper is devoted to the advances obtained by the theory of strict polynomial functors initiated by…
These are notes on twisted K-homology theory and twisted Ext-theory from the C*-algebra viewpoint, part of a series of talks on ``C*-algebras, noncommutative geometry and K-theory'', primarily for physicists.
We describe a bordered version of totally twisted Khovanov homology. We first twist Roberts's type $D$ structure by adding a "vertical" type $D$ structure which generalizes the vertical map in twisted tangle homology. One of the distinct…
The quandle homology theory is generalized to the case when the coefficient groups admit the structure of Alexander quandles, by including an action of the infinite cyclic group in the boundary operator. Theories of Alexander extensions of…
This paper introduces the notion of twisted toric manifolds which is a generalization of one of symplectic toric manifolds, and proves the weak Delzant type classification theorem for them. The computation methods for their fundamental…
We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted cohomology, twisted $K$-theory and Courant…
Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…
This thesis captures the ongoing development of twisted cubes, which is a modification of cubes (in a topological sense) where its homotopy type theory does not require paths or higher paths to be invertible. My original motivation to…
We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class $\mathcal{C}$ of Fujiki. We give a Hodge-theoretical proof of the…
In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized K\"ahler…
We introduce mixed twistor $D$-modules, and establish the fundamental functorial property. We also prove that they are described as the gluing of admissible variations of mixed twistor structure. In a sense, mixed twistor $D$-modules could…
We explore the relations of twisted K-theory to twisted and untwisted classical cohomology. We construct an Atiyah-Hirzebruch spectral sequence, and describe its differentials rationally as Massey products. We define the twisted Chern…
Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…