Related papers: A Subgroup Theorem for Homological Filling Functio…

Some boundedness properties of function spaces (considered as topological groups) are studied.

Let G be a semisimple Lie group with no compact factors, K a maximal compact subgroup of G, and $\Gamma$ a lattice in G. We study automorphic forms for $\Gamma$ if G is of real rank one with some additional assumptions, using dynamical…

For every natural number k we introduce the notion of k-th order convolution of functions on abelian groups. We study the group of convolution preserving automorphisms of function algebras in the limit. It turns out that such groups have…

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a…

In our articles of recent years, the technique of gluing two subharmonic functions turned out to be very useful in studying the distribution of the roots or masses of holomorphic or subharmonic functions, respectively. Here we develop and…

Given a finite group $G$ acting on a surface $S$, the centralizer of G in the mapping class group $\textrm{Mod}(S)$ has a natural representation given by its action on the homology $H_1(S; \mathbb{Q})$. We consider the question of whether…

We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special…

For a commutative ring $R$ with a unit, an $R$-homology rose is a topological space whose homology groups with $R$-coefficients agree with those of a bouquet of cirlces. In this paper, we study some special properties of covering spaces and…

Filling functions are asymptotic invariants of finitely presentable groups; the seminal work on the subject is by M.Gromov. They record features of combinatorial homotopy discs (van Kampen diagrams) filling loops in Cayley 2-complexes.…

Let $k$ be a noetherian commutative ring and let $G$ be a finite flat group scheme over $k$. Let $G$ act rationally on a finitely generated commutative $k$-algebra $A$. We show that the cohomology algebra $H^*(G,A)$ is a finitely generated…

We consider space functions $s(n)$ of finitely presented groups $G =< A\mid R> .$ (These functions have a natural geometric analog.) To define $s(n)$ we start with a word $w$ over $A$ of length at most $n$ equal to 1 in $G$ and use…

Let $R=\mathbb{F}_p$ or a field of characteristic $0$. For each $R$-good topological space $Y$, we define a collection of higher cohomology operations which, together with the cohomology algebra $H^*(Y;R)$ suffice to determine $Y$ up to…

We establish new strong lower bounds on the (subnormal) subgroup growth of a large class of groups. This includes the fundamental groups of all finite-volume hyperbolic 3-manifolds and all (free non-abelian)-by-cyclic groups. The lower…

A function field over a finite field is called maximal if it achieves the Hasse-Weil bound. Finding possible genera that maximal function fields achieve has both theoretical interest and practical applications to coding theory and other…

The first part of the paper is a brief overview of Hindman's finite sums theorem, its prehistory and a few of its further generalizations, and a modern technique used in proving these and similar results, which is based on idempotent…

Hom-groups are nonassociative generalizations of groups where the unitality and associativity are twisted by a map. We show that a Hom-group (G, {\alpha}) is a pointed idempotent quasigroup (pique). We use Cayley table of quasigroups to…

We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, {\em if-then-else} and…

We introduce the term "protonormal" to refer to a subgroup H of a group G such that for every x in G the subgroups x^{-1}Hx and H commute as sets. If moreover (G,H) is a Hecke pair we show that the Hecke algebra H(G,H) is generated by the…

Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group of a closed hyperbolic surface, or Out(F_n) for n>1). We…

We prove that the word problem of a finitely generated group $G$ is in NP (solvable in polynomial time by a non-deterministic Turing machine) if and only if this group is a subgroup of a finitely presented group $H$ with polynomial…