Related papers: An isomorphism theorem for Alexander biquandles

This paper extends Alexander duality to the setting of parametrized homology. Let X with be a compact subset of R^n x R (n \geq 2) satisfying certain conditions, let Y be its complement, and let p be the projection onto the second factor.…

First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…

We show that two simple, separable, nuclear and $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras are isomorphic if they are trace-preservingly homotopy equivalent. This result does not assume the UCT and can be viewed as a tracial stably…

Let $A$ be a commutative ring with unity, and $M$ a finitely generated $A$-module. In 1971, Morris Orzech showed that any surjective $A$-module homomorphism from a submodule of $M$ to $M$ must be an isomorphism. We give a constructive proof…

This paper is devoted to characterizing the so-called order isomorphisms intertwining the $L^2$-semigroups of two Dirichlet forms. We first show that every unitary order isomorphism intertwining semigroups is the composition of…

The Alexander biquandle of a virtual knot or link is a module over a 2-variable Laurent polynomial ring which is an invariant of virtual knots and links. The elementary ideals of this module are then invariants of virtual isotopy which…

Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known…

If phi: G-->G' is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G'. As an application, we show non-existence of surjective homomorphism between certain…

We study the relation between module and Hochschild cohomology groups of Banach algebras with a compatible module structure. More precisely, we show that for every commutative Banach $ \mathcal{A} $-$ \mathfrak{A}$-bimodule $ X $ and every…

We extend the notion of link colorings with values in an Alexander quandle to link colorings with values in a module $M$ over the Laurent polynomial ring $\Lambda_{\mu}=\mathbb{Z}[t_1^{\pm1},\dots,t_{\mu}^{\pm1}]$. If $D$ is a diagram of a…

We define an equivalence relation between bimodules over maximal abelian selfadjoint algebras (masa bimodules) which we call spatial Morita equivalence. We prove that two reflexive masa bimodules are spatially Morita equivalent iff their…

The main goal of this article is to study the cohomology rings and their applications of moment-angle complexes associated to Gorenstein* complexes, especially, the applications in combinatorial commutative algebra and combinatorics. First,…

In our preceding paper we have introduced the notion of an $s$-homogeneous triple. In this paper we use this technique to study connected $s$-homogeneous algebras with two relations. For such algebras, we describe all possible pairs…

Concerns decompositions of smooth 4-manifolds as the union of two handlebodies, each with handles of index <=2 (``Heegard'' decompositions).Sample result: Two 2-complexes are (up to 2-deformation) dual spines of a Heegard decomposition of…

We show that if (M,E,E') satisfies the first order Zermelo-Fraenkel axioms of set theory when the membership relation is E and also when the membership relation is E', and in both cases the formulas are allowed to contain both E and E',…

Let X be a "nice" space with an action of a torus T. We consider the Atiyah-Bredon sequence of equivariant cohomology modules arising from the filtration of X by orbit dimension. We show that a front piece of this sequence is exact if and…

Let $k$ be a field of characteristic not equal to $2,3$, $\mathbb{O}$ an octonion over $k$ and $\mathcal{J}$ the exceptional Jordan algebra defined by $\mathbb{O}$. We consider the prehomogeneous vector space $(G,V)$ where $G=GE_6\times…

For i=1,2, let (M_i,D_i) be pairs consisting of a Cartan MASA D_i in a von Neumann algebra M_i, let atom(D_i) be the set of atoms of D_i, and let S_i be the lattice of Bures-closed D_i bimodules in M_i. We show that when M_i have separable…

A bipartite graph $G=(V,E)$ with $V=V_1\cup V_2$ is biregular if all the vertices of each stable set, $V_1$ and $V_2$, have the same degree, $r$ and $s$, respectively. This paper studies difference sets derived from both Abelian and…

Let $V$ be a simple vertex algebra of countable dimension, $G$ be a finite automorphism group of $V$ and $\sigma$ be a central element of $G$. Assume that ${\cal S}$ is a finite set of inequivalent irreducible $\sigma$-twisted $V$-modules…