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The main result of this work is a new proof and generalization of Lazard's comparison theorem of locally analytic group cohomology with Lie algebra cohomology for K-Lie groups, where K is a finite extension of the p-adic numbers. We show…
In general a universal covering of a non connected topological group need not admit a topological group structure such that the covering map is a morphism of topological groups. This result is due to R.L. Taylor (1953). We generalise this…
The category of crossed complexes gives an algebraic model of CW-complexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
We show that there are homotopy equivalences $h:N\to M$ between closed manifolds which are induced by cell-like maps $p:N\to X$ and $q:M\to X$ but which are not homotopic to homeomorphisms. The phenomenon is based on construction of…
The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the…
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
We formulate and analyze several finiteness conjectures for linear algebraic groups over higher-dimensional fields. In fact, we prove all of these conjectures for algebraic tori as well as in some other situations. This work relies in an…
A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of…
We explore equilibrium solutions of non-topological solitons in a general class of scalar field theories which include global U(1) symmetry. We find new types of solutions, tube-shaped and crust-shaped objects, and investigate their…
This work deals with charged nontopological solutions that appear in relativistic models described by a single complex scalar field in two-dimensional spacetime. We study a model which supports novel analytical configurations of the Q-ball…
We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.
We give a new technique for constructing presentations by generators and relations for representations of groups like $SL_n(\mathbb{Z})$ and $Sp_{2g}(\mathbb{Z})$. Our results play an important role in recent work of the authors calculating…
We prove new homological stability results for general linear groups over finite fields. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category of $E_\infty$-algebras, guided…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
This replacement corrects statement and proof of the main result. Also, a section on the universal Abel-Jacobi map has been added.
We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing families of indecomposable representations from indecomposables…
We show that the equation associated with a group word $w \in G \ast {\mathbf F}_2$ can be solved over a hyperlinear group $G$ if its content - that is its augmentation in ${\mathbf F}_2$ - does not lie in the second term of the lower…
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…
We offer a direct proof of an elementary result concerning cohomological periods. As a corollary we show that given a finitely generated stably free resolution of Z over a finite group, two of its modules are free.