Related papers: A Geometric Model for Odd Differential K-theory
We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…
The Quillen-Bismut-Freed construction associates a determinant line bundle with connection to an infinite dimensional super vector bundle with a family of Dirac-type operators. We define the regularized first Chern form of the infinite…
Let $f: X \to S$ be flat morphism over an algebraically closed field $k$ with a relative normal crossings divisor $Y\subset X$, $(E, \nabla)$ be a bundle with a connection with log poles along $Y$ and curvature with values in…
The purpose of this paper is to extend our previous work on the variational formula for the Bismut-Cheeger eta form without the kernel bundle assumption by allowing the spin$^c$ Dirac operators to be twisted by isomorphic vector bundles,…
We consider the cobordism ring of involutions of a field of characteristic not two, whose elements are formal differences of classes of smooth projective varieties equipped with an involution, and relations arise from equivariant K-theory…
For any positive integer $n$ and any Lie group $\mathfrak{G}$, given a definite symmetric bilinear form on $\mathbb{R}^n$ and an $\hbox{Ad}$-invariant scalar product on the Lie algebra of $\mathfrak{G}$, we construct a variational problem…
The observable properties of topological quantum matter are often described by topological field theories. We here demonstrate that this principle extends beyond thermal equilibrium. To this end, we construct a model of two-dimensional…
This is a review/announcement of results concerning the connection between certain exactly solvable two-dimensional models of statistical mechanics, namely loop models, and the equivariant $K$-theory of the cotangent bundle of the…
In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles over exceptional Grassmannians in terms of their associated data. We show that there are only finitely many irreducible homogeneous ACM bundles by…
We outline in detail the general caloron correspondence for the group of automorphisms of an arbitrary principal $G$-bundle $Q$ over a manifold $X$, including the case of the gauge group of $Q$. These results are used to define…
We provide a systematic approach to twisting differential KO-theory leading to a construction of the corresponding twisted differential Atiyah-Hirzebruch spectral sequence (AHSS). We relate and contrast the degree two and the degree one…
In this paper we identify QD(A,B), the quasidiagonal classes in KK_1(A,B), in terms of K_*(A) and K_*(B), and we use these results in various applications. Here is our central result. Theorem: Suppose that A is in the category of separable…
A cocycle $\Omega: P \times G \to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$…
We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we call "cohesive". Cocycles in this…
We consider the mixed gravitational-Yang-Mills anomaly as the coupling between the $K$-theory and $K$-homology of a $C^*$-algebra crossed product. The index theorem of Connes-Moscovici allows to compute the Chern character of the $K$-cycle…
In this paper we first prove that every differential character can be represented by differential form with singularities. Then we lift the Gauss-Bonnet-Chern theorem for vector bundles to differential characters.
The fourth paper of our series of papers entitled "Differential Geometry of Microlinear Frolicher Spaces is concerned with jet bundles. We present three distinct approaches together with transmogrifications of the first into the second and…
We state a precise conjectural isomorphism between localizations of the equivariant quantum K-theory ring of a flag variety and the equivariant K-homology ring of the affine Grassmannian, in particular relating their Schubert bases and…
We show that Berezinskii's classification of the symmetries of Cooper pair amplitudes holds for driven systems even in the absence of translation invariance. We then consider a model Hamiltonian for a superconductor coupled to an external…
The refined Chern-Simons theory is a one-parameter deformation of the ordinary Chern-Simons theory on Seifert manifolds. It is defined via an index of the theory on N M5 branes, where the corresponding one-parameter deformation is a natural…