Related papers: Expansion of a simplicial complex

We show that Sullivan's model of rational differential forms on a simplicial set $X$ may be interpreted as a (kind of) $0|1$-dimensional supersymmetric quantum field theory over $X$, and, as a consequence, concordance classes of such…

We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…

We generalize the fundamental graph-theoretic notion of chordality for higher dimensional simplicial complexes by putting it into a proper context within homology theory. We generalize some of the classical results of graph chordality to…

We quantify the topological expansion properties of bounded degree simplicial complexes in terms of a family of sublinear functions, in analogy with the separation profile of Benjamini-Schramm-Tim\'ar for classical expansion of bounded…

Expander graphs in general, and Ramanujan graphs in particular, have been of great interest in the last three decades with many applications in computer science, combinatorics and even pure mathematics. In these notes we describe various…

We first develop a general framework for Laplace operators defined in terms of the combinatorial structure of a simplicial complex. This includes, among others, the graph Laplacian, the combinatorial Laplacian on simplicial complexes, the…

We introduce new simplicial complexes by using various invariants and local moves for knots, which give generalizations of the Gordian complex defined by Hirasawa and Uchida. In particular, we focus on the simplicial complex defined by…

It is shown that the notion of W_\infty-algebra originally carried out over a (compact) Riemann surface can be extended to n complex dimensional (compact) manifolds within a symplectic geometrical setup. The relationships with the…

The Circle Pattern Theorem characterizes the existence and rigidity of circle patterns with prescribed intersection angles on simplicial triangulations of closed surfaces. In this paper we extend the theorem to quasi-simplicial…

We give a bound for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive a bound for the Betti numbers of iterated stellar…

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The…

Combining V. Koziarz's observation about the regularity of some modified section related to the initial extension with J. McNeal--D. Varolin's regularity argument, we generalize two theorems of McNeal--Varolin for the $L^2$ extension of…

For several important classes of manifolds acted on by the torus, the information about the action can be encoded combinatorially by a regular n-valent graph with vector labels on its edges, which we refer to as the torus graph. By analogy…

For graphs there exists a strong connection between spectral and combinatorial expansion properties. This is expressed, e.g., by the discrete Cheeger inequality, the lower bound of which states that $\lambda(G) \leq h(G)$, where…

We expand the Chebyshev polynomials and some of its linear combination in linear combinations of the q-Hermite, the Rogers (q-utraspherical) and the Al-Salam--Chihara polynomials and vice versa. We use these expansions to obtain expansions…

We recently introduced a notion of tilings of geometric realizations of finite relative simplicial complexes and related those tilings to the discrete Morse theory of R. Forman, especially when they have the property of being shellable, a…

We calculate the determinant of the bilinear form in middle degree of the generic artinian reduction of the Stanley-Reisner ring of an odd-dimensional simplicial sphere. This proves the odd multiplicity conjecture of Papadakis and Petrotou…

We construct explicit generating sets S_n and \tilde S_n of the for the alternating and the symmetric groups, which turn the Cayley graphs C(Alt(n), S_n) and C(Sym(n), \tilde S_n) into a family of bounded degree expanders for all n. This…

We develop prismatic and syntomic cohomology relative to a $\delta$-ring. This simultaneously generalizes Bhatt and Scholze's absolute and relative prismatic cohomology and shows that the latter, which was defined relative to a prism, is in…

Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…