相关论文: Virtual Localization in equivariant Witt cohomolog…

We give details of models for rational torus equivariant homotopy theory based on (a) all subgroups, connected subgroups or dimensions of subgroups and (b) on pairs or general flags. We provide comparison functors and show the models are…

For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\subset X$ is an embedded curve and $D\subset C$ is a divisor. A virtual class is constructed on the associated moduli space…

This paper investigates the Witt groups of triangulated categories of sheaves (of modules over a ring R in which 2 is invertible) equipped with Poincare-Verdier duality. We consider two main cases, that of perfect complexes of sheaves on…

Given certain intersection cohomology sheaves on a projective variety with a torus action, we relate the cohomology groups of their tensor product to the cohomology groups of the individual sheaves. We also prove a similar result in the…

We present a higher index theorem for a certain class of etale one-dimensional complex-analytic groupoids. The novelty is the use of the local anomaly formula established in a previous paper, which represents the bivariant Chern character…

For a $G$-scheme $X$ with a given equivariant perfect obstruction theory, we prove a virtual equivariant Grothendieck-Riemann-Roch formula, this is an extension of a result of Fantechi-G\"ottsche to the equivariant context. We also prove a…

We reprove and generalize the result that the intersection cohomology groups of a toric variety with coefficient in a nontrivial rank one local system vanish. We prove a similar vanishing result for a certain class of varieties on which a…

The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordisms which directly applies to classical knot and classical…

Let $G$ be the product $GL_r(C) \times (C^\times)^n$. We show that the $G$-equivariant Chow class of a $G$ orbit closure in the space of $r$-by-$n$ matrices is determined by a matroid. To do this, we split the natural surjective map from…

We study the space of conjugacy classes of subgroups of a compact Lie group G whose identity component is a torus, and consider how various invariants of subgroups behave as sheaves over this space. This feeds in to the author's programme…

The aim of this article is to introduce Vogel's localization theorem for classes of D-complexes: this generalization of Waldhausen's localization theorem is especially useful and powerful in that it gives an explicit and computable…

We construct virtual fundamental classes for dg-manifolds whose tangent sheaves have cohomology only in degrees 0 and 1. This condition is analogous to the existence of a perfect obstruction theory in the approach of Behrend-Fantechi [BF]…

Lurie and Gepner--Meier each define equivariant cohomology theories, namely \emph{tempered cohomology} and \emph{equivariant elliptic cohomology}, respectively, using derived algebraic geometry. We construct a natural equivalence between…

There is a standard method to calculate the cohomology of torus-invariant sheaves $L$ on a toric variety via the simplicial cohomology of associated subsets $V(L)$ of the space $N_{\mathbb R}$ of 1-parameter subgroups of the torus. For a…

Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. This paper is a survey, and does not contain any new results.…

An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work…

Recent results by Spitters et. al. suggest that quantum phase space can usefully be regarded as a ringed topos via a process called Bohrification. They show that quantum kinematics can then be interpreted as classical kinematics, internal…

We define the Chow ring of the classifying space of a linear algebraic group. In all the examples where we can compute it, such as the symmetric groups and the orthogonal groups, it is isomorphic to a natural quotient of the complex…

We extend the scope of Balmer's tensor triangular Chow groups to compactly generated triangulated categories $\mathcal{K}$ that only admit an action by a compactly-rigidly generated tensor triangulated category $\mathcal{T}$ as opposed to…

This thesis splits into two major parts. The connection between the two parts is the notion of "categorification" which we shortly explain/recall in the introduction. In the first part of this thesis we extend Bar-Natan's cobordism based…