Related papers: Vertical Genera
We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
We compute the cohomology of the stack M_1 with coefficients in Z[1/2], and in low degrees with coefficients in Z. Cohomology classes on M_1 give rise to characteristic classes, cohomological invariants of families of curves of genus one.…
Kotschick and Morita recently discovered factorisations of characteristic classes of transversally symplectic foliations that yield new characteristic classes in foliated cohomology. We describe an alternative construction of such…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
Given a Riemann surface and a riemannian manifold M with certain restrictions, we construct a cobordism invariant of M. This invariant is a generalization of the elliptic genus and it shares some similar properties.
We construct a ring structure on complex cobordism tensored with the rationals, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-…
This note discusses some examples showing that the crystalline cohomology of even very mildly singular projective varieties tends to be quite large. In particular, any singular projective variety with at worst ordinary double points has…
We study a family of subrings, indexed by the natural numbers, of the mod-p cohomology of a finite group G. These subrings are based on a family of v_n-periodic complex oriented cohomology theories and are constructed as rings of…
The paper establishes new relationship between cohomology, extensions and automorphisms of quandles. We derive a four term exact sequence relating quandle 1-cocycles, second quandle cohomology and certain group of automorphisms of an…
We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. As an…
The cohomology of the degree-$n$ general linear group over a finite field of characteristic $p$, with coefficients also in characteristic $p$, remains poorly understood. For example, the lowest degree previously known to contain nontrivial…
We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so called (derived) Hochschild complex of a morphism; the…
Using the path lattice cohomology we provide a conceptual topological characterization of the geometric genus for certain complex normal surface singularities with rational homology sphere links, which is uniformly valid for all…
The characteristic forms in the bundle of connections of a principal bundle P over M determine the characteristic classes of P for degree less or equal to the dimension of M, and differential forms on the space of connections for higher…
The article presents four reasons why the elliptic genus is the most general characteristic class that admits a generalization to singular spaces. We prove that the elliptic characteristic class (with an additional factor) is essentially…
We generalize Kontsevich's construction of characteristic classes of fibre bundles with homology sphere fibres and a trivialization of the vertical tangent bundle to framed fibre bundles with closed manifold fibres.
For an infinite chain bicomplex we show that the orthogonality and grading conditions provide it with the structure of a bigraded differential algebra with respect to a natural multiplication of several elements bicomplex spaces.…
We obtain relations among the characteristic classes of a manifold M admitting corank one maps. Our relations yield strong restrictions on the cobordism class of M and also nonexistence results for singular maps of the projective spaces. We…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…