Related papers: Parametrized Euler class and semicohomology theory

A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…

In this work we construct an extension for the category of 0-modules by analogy with [H.-J. Baues and G. Wirshing, Cohomology of small categories, J. Pure Appl. Algebra, 38(1985), 187-211]. The 0-cohomology functor becomes a derived functor…

We begin by reviewing the definition of 3-Lie algebras and the fundamental concepts of matched pairs. Subsequently, we introduce the representation theory of matched pairs and define the semidirect product. Building on this foundation, we…

We describe the projectives in the category of functors from a graded poset to abelian groups. Based on this description we define a related condition, pseudo-projectivity, and we prove that this condition is enough for the vanishing of the…

Ghys established the relationship between the bounded Euler class in $H_{b}^{2}(\mathrm{Homeo}_{+}(S^{1});\mathbb{Z})$ and the Poincar\'{e} rotation number, that is, he proved that the pullback of the bounded Euler class under a…

We give a construction of non-ordinary $p$-adic families of classes in the cohomology of locally symmetric spaces associated to spherical pairs of reductive groups. In the \'etale case, we show how to map these classes into Galois…

We show that the category of numerically generated pointed spaces is complete, cocomplete, and monoidally closed with respect to the smash product, and then utilize these features to establish a simple but flexible method for constructing…

Let $\mathcal{X}_S$ denote the class of spaces homeomorphic to two closed orientable surfaces of genus greater than one identified to each other along an essential simple closed curve in each surface. Let $\mathcal{C}_S$ denote the set of…

We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong…

We construct an Euler system associated to regular algebraic, essentially conjugate self-dual cuspidal automorphic representations of GL(3) over imaginary quadratic fields, using the cohomology of Shimura varieties for GU(2, 1).

On any manifold M^n, the de Rham operator D=d+d^* (with respect to a complete Riemannian metric), with the grading of forms by parity of degree, gives rise by Kasparov theory to a class [D] in KO_0(M), which when M is closed maps to the…

We give rigorous foundations for parametrized homotopy theory in this monograph. After preliminaries on point-set topology, base change functors, and proper actions of non-compact Lie groups, we develop the homotopy theory of equivariant…

We show that in any symmetric monoidal category, if a weight for colimits is absolute, then the resulting colimit of any diagram of dualizable objects is again dualizable. Moreover, in this case, if an endomorphism of the colimit is induced…

Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…

We follow the same technics we used before in \cite{AZ} of extending knot Floer homology to embedded graphs in a 3-manifold, by using the Kauffman topological invariant of embedded graphs by associating family of links and knots to a such…

In this paper we study general hyperplane sections of adjoint and coadjoint varieties. We show that these are the only sections of homogeneous varieties such that a maximal torus of the automorphism group of the ambient variety stabilizes…

Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain estimates of the (co)homological dimension of groups G…

We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent…

Let $G$ be the simple algebraic group $\mathrm{SL}_2$ defined over an algebraically closed field $k$ of characteristic $p > 0$. Using results of A. Parker, we develop a method which gives, for any $q \in \mathbb{N}$, a closed form…

We show that the Hochschild cohomology of a monomial algebra over a field of characteristic zero vanishes from degree two if the first Hochschild cohomology is semisimple as a Lie algebra. We also prove that first Hochschild cohomology of a…