相关论文: Discrete Morse Theory for free chain complexes

Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete analogue of the stratified Morse theory of Goresky and…

This paper shows that discrete Morse-Bott theory can be developed as a natural extension of R. Forman's discrete Morse theory by improving the definition of the discrete Morse-Bott function introduced by S. Yaptieu. To this end, we…

We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C*-algebra has a…

We introduce the notion of a Morse sequence, which provides a simple and effective approach to discrete Morse theory. A Morse sequence is a sequence composed solely of two elementary operations, that is, expansions (the inverse of a…

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…

In this paper, we prove that discrete Morse functions on digraphs are flat Witten-Morse functions and Witten complexes of transitive digraphs approach to Morse complexes. We construct a chain complex consisting of the formal linear…

We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…

For a finite simplicial complex K and a CW-pair (X,A), there is an associated CW-complex Z_K(X,A), known as a polyhedral product. We apply discrete Morse theory to a particular CW-structure on the n-sphere moment-angle complexes Z_K(D^{n},…

We investigate properties of the set of discrete Morse functions on a simplicial complex as defined by Forman. It is not difficult to see that the pairings of discrete Morse functions of a finite simplicial complex again form a simplicial…

We introduce the notion of mixed subtree quasi-isometries, which are self quasi-isometries of regular trees built in a specific inductive way. We then show that any self quasi-isometry of a regular tree is at bounded distance from a…

We prove that the class of crossed product C*-algebras associated with the action of the multiplicative group of a number field on its ring of finite adeles is rigid in the following explicit sense: Given any *-isomorphism between two such…

We develop functoriality for Morse theory, namely, to a pair of Morse-Smale systems and a generic smooth map between the underlying manifolds we associate a chain map between the corresponding Morse complexes, which descends to the correct…

We extend the classical Feferman-Vaught theorem to logic for metric structures. This implies that the reduced powers of elementarily equivalent structures are elementarily equivalent, and therefore they are isomorphic under the Continuum…

Forman's Discrete Morse theory is studied from an algebraic viewpoint. Analogous to independent work of Emil Skoeldberg we show that this theory can be extended to chain complexes of free modules over a ring. We provide three applications…

The literature provides dichotomies involving homomorphisms (like the G 0 dichotomy) or reductions (like the characterization of sets potentially in a Wadge class of Borel sets, which holds on a subset of a product). However, part of the…

Incidence relations among the cells of a regular CW complex produce a poset-enriched category of entrance paths whose classifying space is homotopy-equivalent to that complex. We show here that each acyclic partial matching (in the sense of…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

We give a short topological proof of coherence for categorified non-symmetric operads by using the fact that the diagrams involved form the 1-skeleton of simply connected CW complexes. We also obtain a "one-step" topological proof of Mac…

For a Morse function f on a compact oriented manifold M, we show that f has more critical points than the number required by the Morse inequalities if and only if there exists a certain class of link in M whose components have nontrivial…

This work investigates the combinatorial structures underlying cyclic conditional freeness and introduces cumulants that serve to linearize the cyclic conditional additive convolution. In the process, we establish the notion of "cyclic…