Related papers: Finite convergent presentation of plactic monoid f…

Let $G$ be a real reductive Lie group, $L$ a compact subgroup, and $\pi$ an irreducible admissible representation of $G$. In this article we prove a necessary and sufficient condition for the finiteness of the multiplicities of $L$-types…

The realization theorem asserts that for a finitely presented group G, the D(2) property and the realization property are equivalent as long as G satisfies a certain finiteness condition. We show that the two properties are in fact…

We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification…

We show that every finite-dimensional p-adic Lie group of class C^k admits a C^k-compatible analytic Lie group structure.

The purpose of this paper is to introduce the theory of presentations of monoids acts. We aim to construct `nice' general presentations for various act constructions pertaining to subacts and Rees quotients. More precisely, given an $M$-act…

Continuing earlier work, we show how to realize irreducible finite-dimensional representations of the complex group of type $G_2$ via tableaux, along the way exhibiting explicit generators of the defining ideal of the flag variety

We prove that compact topological 4-manifolds can be effectively presented by a finite amount of data.

We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.

Assuming that every hyperbolic group is residually finite, we prove the congruence subgroup property for mapping class groups of hyperbolic surfaces of finite type. Under the same assumption, it follows that profinitely equivalent…

We prove that every finite semigroup embeds in a finitely presented congruence-free monoid, and pose some questions around the Boone-Higman Conjecture.

We study the class of monoids that arise as the submonoid of right units of finitely presented special inverse monoids (SIMs). Gray and Ru\v{s}kuc (2024) gave the first example of a finitely presented SIM whose submonoid of right units does…

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…

We develop a method of calculation for the symplectic Floer homology of composite knots. The symplectic Floer homology of knots defined in \cite{li} naturally admits an integer graded lifting, and it formulates a filtration and induced…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},\ldots , a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}\cdots a_{n} =a_{\sigma (1)} a_{\sigma (2)} \cdots a_{\sigma (n)}$, where…

This paper demonstrates the uniformly finite homology developed by Block and Weinberger and its relationship to amenable spaces via applications to the Cayley graph of Thompson's Group F. In particular, a certain class of subgraph of F is…

In this article we introduce the space of configurations of commuting elements in a topological group and show that it satisfies rational homological stability for the sequences of unitary, special unitary and symplectic groups. We also…

We give new, short proofs of the presentations for the partition monoid and its singular ideal originally given in the author's 2011 papers in J Alg and IJAC.

We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free…

We consider symplectic singularities in the sense of A. Beauville as examples of Poisson schemes. Using Poisson methods, we prove that a symplectic singularity admits a finite stratification with smooth symplectic strata. We also prove that…

We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of…