相关论文: Periodicity and the determinant bundle

The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…

We construct the algebraic cobordism theory of bundles and divisors on smooth varieties. It has a simple basis (over Q) from projective spaces and its rank is equal to the number of Chern invariants. As an application we study the number of…

We apply the equivariance --> families principle to a geometric family of Clifford module bundles with an action of a compact Lie group G to prove an equivariant version of Bismut's families index theorem on the differential Borel quotient…

To each irreducible infinite dimensional representation $(\pi,\cH)$ of a $C^*$-algebra $\cA$, we associate a collection of irreducible norm-continuous unitary representations $\pi_{\lambda}^\cA$ of its unitary group $\U(\cA)$, whose…

Let $\mathscr{V}\mathrm{ect}_n$ be the moduli stack of vector bundles of rank $n$ on schemes. We prove that, if $E$ is a Zariski sheaf of ring spectra which is equipped with finite quasi-smooth transfers and satisfies the projective bundle…

By using the notion of a rigid R-matrix in a monoidal category and the Reshetikhin--Turaev functor on the category of tangles, we review the definition of the associated invariant of long knots. In the framework of the monoidal categories…

We consider the finite generation property for cohomology of a finite tensor category C, which requires that the self-extension algebra of the unit Ext*_C(1,1) is a finitely generated algebra and that, for each object V in C, the graded…

Let $M$ be a hyperkahler manifold, $\Gamma$ its mapping class group, and $Teich$ the Teichmuller space of complex structures of hyperkahler type. After we glue together birationally equivalent points, we obtain the so-called birational…

In this paper, we establish a precise connection between higher rho invariants and delocalized eta invariants. Given an element in a discrete group, if its conjugacy class has polynomial growth, then there is a natural trace map on the…

Using determinant functor, we describe a natural transformation from local Hilbert functor to K-theoretic cycle groups of codimension one, which were variants of Balmer's tensor triangular Chow groups. This enables us to answers a question…

We provide a generalization to the higher dimensional case of the construction of the current algebra g((z)), of its Kac-Moody extension and of the classical results relating them to the theory of G-bundles over a curve. For a reductive…

Billey and Braden defined a geometric pattern map on flag manifolds which extends the generalized pattern map of Billey and Postnikov on Weyl groups. The interaction of this torus equivariant map with the Bruhat order and its action on line…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

We present a new family of monads whose cohomology is a stable rank two vector bundle on $\mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used…

K-theoretic Gromov-Witten invariants of a compact Kahler manifold $X$ are defined as super-dimensions of sheaf cohomology of interesting bundles over moduli spaces of n-pointed holomorphic curves in X. With this article, we begin a series…

We show that an asymptotic property of the determinants of certain matrices whose entries are finite sums of cotangents with rational arguments is equivalent to the GRH for odd Dirichlet characters. This is then connected to the existence…

The knot coloring polynomial defined by Eisermann for a finite pointed group is generalized to an infinite pointed group as the longitudinal mapping invariant of a knot. In turn this can be thought of as a generalization of the quandle…

We explain the relationship between various characteristic classes for smooth manifold bundles known as ``higher torsion'' classes. We isolate two fundamental properties that these cohomology classes may or may not have: additivity and…

V.F. Molchanov considered the Hilbert series for the space of invariant skew-symmetric tensors and dual tensors with polynomial coefficients under the action of a real reflection group, and speculated that it had a certain product formula…

We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalizes the Dixmier-Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As…