Related papers: Mapping cone Thom forms

Let r be an orbit of the quiver representation of type A_n (equioriented case). In this paper we study the Poincare dual of the closure of r (a.c.a. Thom polynomial/degeneracy loci formula) in equivariant cohomology. Using general Thom…

We study the deformation theory of morphisms of properads and props thereby extending to a non-linear framework Quillen's deformation theory for commutative rings. The associated chain complex is endowed with a Lie algebra up to homotopy…

We study the interplay between the Fourier-Mukai transform and the decomposition theorem for an integrable system $\pi: M \rightarrow B$. Our main conjecture is that the Fourier-Mukai transform of sheaves of K\"ahler differentials, after…

A classical result of A. Connes asserts that the Frechet algebra of smooth functions on a smooth compact manifold X provides, by a purely algebraic procedure, the de Rham cohomology of X. Namely the procedure uses Hochschild and cyclic…

We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of…

We introduce exponential complexes of sheaves on manifolds. They are resolutions of the (Tate twisted) constant sheaves of the rational numbers, generalising the short exact exponential sequence. There are canonical maps from the…

In a previous article (J. Algebra 367 (2012), 142-165) we established axiomatic parametrised Cohen-Macaulay approximation which in particular was applied to pairs consisting of a finite type flat family of Cohen-Macaulay rings and modules.…

We show that in the mapping class group of a surface any relation between Dehn twists of the form T_x^j T_y^k = M (M a multitwist) is the lantern relation, and any relation of the form (T_x T_y)^k = M (where T_x commutes with M) is the…

In this thesis we examine a set of foundational questions concerning closed forms in superspace. By reformulating a number of definitions through the use of a new ring of (anti-)commuting variables and the concept of an exact Bianchi form,…

We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces. The main approach is…

We provide algorithms for computing the Rochlin invariants of mod 2 homology spheres and mapping tori. This provides a unified framework for studying two families of maps: the Birman-Craggs maps of the Torelli group, and Sato's maps of the…

Given a very ample line bundle on a smooth projective variety, the variation of Hodge structure associated to the universal family of hyperplane sections can be thought of as a $D$-module with action generated by the Gauss-Manin connection.…

For conic bundles on a smooth variety (over a field of characteristic $\ne 2$) which degenerate into pairs of distinct lines over geometric points of a smooth divisor, we prove a theorem which relates the Brauer class of the non-degenerate…

We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We…

Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential…

Configuration space integrals are powerful tools for studying the homotopy type of the space of long embeddings in terms of a combinatorial object called a graph complex. It is unknown whether these integrals give a cochain map due to…

We introduce the conormal fan of a matroid M, which is a Lagrangian analog of the Bergman fan of M. We use the conormal fan to give a Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of M. This allows us to express the…

We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan…

In this article, we prove a generalization of a theorem of Lisca-Matic to Stein cobordisms and develop a method for distinguishing certain Stein cobordisms using rotation numbers. Using these results along with standard techniques from…

We examine the five-dimensional super-de Rham complex with $N = 1$ supersymmetry. The elements of this complex are presented explicitly and related to those of the six-dimensional complex in $N = (1, 0)$ superspace through a specific notion…