Related papers: Bundle gerbes on supermanifolds

A $\mathbb Q$-conic bundle germ is a proper morphism from a threefold with only terminal singularities to the germ $(Z \ni o)$ of a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We obtain…

For every imprimitive complex reflection group of rank 2, we construct a semi-orthogonal decomposition of the derived category of the associated global quotient stack which categorifies the usual decomposition of the orbifold cohomology…

We determine generators of the rational cohomology algebras of moduli spaces of parabolic vector bundles on a curve, under some `primality' conditions on the parabolic datum. These generators are canonical in a precise sense. Our results…

The bigerbes introduced here give a refinement of the notion of 2-gerbes, representing degree four integral cohomology classes of a space. Defined in terms of bisimplicial line bundles, bigerbes have a symmetry with respect to which they…

We study the structure of finite quandles in terms of subquandles. Every finite quandle $Q$ decomposes in a natural way as a union of disjoint $Q$-complemented subquandles; this decomposition coincides with the usual orbit decomposition of…

The deformation bicomplex of a module-algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module-coalgebras,…

Let X be a compact Kaehler manifold. We expect that any direct sum decomposition of the tangent bundle T(X) comes from a splitting of the universal covering space of X as a product of manifolds, in such a way that the given decomposition of…

We discuss various lifting and reduction problems for bundles and gerbes in the context of a strict Lie 2-group. We obtain a geometrical formulation (and a new proof) for the exactness of Breen's long exact sequence in non-abelian…

Within its traditional range of perversity parameters, intersection cohomology is a topological invariant of pseudomanifolds. This is no longer true once one allows superperversities, in which case intersection cohomology may depend on the…

We present a general theorem which computes the cohomology of a homological vector field on global sections of vector bundles over smooth affine supervarieties. The hypotheses and results have the clear flavor of a localization theorem.

We show that the inertia stack of a topological stack is again a topological stack. We further observe that the inertia stack of an orbispace is again an orbispace. We show how a U(1)-banded gerbe over an orbispace gives rise to a flat line…

We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem…

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…

We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for the direct image of the intersection cohomology complex under a proper map of complex algebraic varieties. The method rests on new…

A generalization to the almost complex setting of a well-known result by S. Webster is given. Namely, we prove that if $\Gamma$ is a strongly pseudoconvex hypersurface in an almost complex manifold $(M, J)$, then the conormal bundle of…

We show that every orthogonal polyhedron of genus at most 2 can be unfolded without overlap while using only a linear number of orthogonal cuts (parallel to the polyhedron edges). This is the first result on unfolding general orthogonal…

This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold…

Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two sub-bundles of the tangent bundle, called the horizontal and vertical bundle. We investigate in these notes…

Let $S$ be a Riemann surface obtained by deleting a finite number of points, called cusps, from a compact Riemann surface. Let $\rho: \pi_1(S)\to Sl(n, \mathbb{C})$ be a semisimple linear representation of $\pi_1(S)$ which is unipotent near…

The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high dimensional manifolds. To be more specific, we study gauge groups of…