Related papers: Discrete Morse Theory for free chain complexes

We study connected components of the Morse boundary and their stabilisers. We introduce the notion of point-convergence and show that if the set of non-singleton connected components of the Morse boundary of a finitely generated group $G$…

We study the matricial field (MF) property for certain reduced crossed product C*-algebras and their traces. Using classification techniques and induced K-theoretic dynamics, we show that reduced crossed products of ASH-algebras of real…

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of…

We use noncommutative localization to construct a chain complex which counts the critical points of a circle-valued Morse function on a manifold, generalizing the Novikov complex. As a consequence we obtain new topological lower bounds on…

We show that an automorphism of an arbitrary CAT(0) cube complex either has a fixed point or preserves some combinatorial axis. It follows that when a group contains a distorted cyclic subgroup, it admits no proper action on a discrete…

The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operator-valued free probability. The paper presents constructions for maps with similar properties to the…

1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…

We compute the K-theory of the C*-algebra of symmetric words in two universal unitaries. This algebra is the fixed point C*-algebra for the order-two automorphism of the full C*-algebra of the free group on two generators which switches the…

In this paper, we introduce a property of topological dynamical systems that we call finite dynamical complexity. For systems with this property, one can in principle compute the $K$-theory of the associated crossed product $C^*$-algebra by…

In this note, we construct invariant and coinvariant Morse chain complexes with integer coefficients for any compact effective orbifold. We show that the homologies of these two chain complexes are invariants of the orbifold. We conjecture…

We give a purely combinatorial proof of a K\"{u}nneth formula for the minus version of knot Floer homology of connected sums by constructing a quasi-isomorphism of grid chain complexes. The quasi-isomorphism naturally deduces that the…

Using free probability constructions involving Cuntz-Pimsner C*-algebras we show that the topological entropy of the free product of two automorphisms is equal to the maximum of the individual entropies. As applications we show that general…

We study the homology of simplicial and cubical sets with symmetries. These are simplicial and cubical sets with additional maps expressing the symmetries of simplices and cubes. We consider the chain complex computing the homology groups…

The topology of the matching complex for the $2\times n$ grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes $\mathrm{Ind}(\Delta_n^m)$ that include these matching complexes. Using this…

Let M be a compact oriented PL manifold and let C_*M be its PL chain complex. The domain of the chain-level intersection pairing is a subcomplex G of C_*M\otimes C_*M. We prove that G is a "full" subcomplex, that is, the inclusion of G in…

In the case of monotone independence, the transparent understanding of the mechanism to validate the central limit theorem (CLT) has been lacking, in sharp contrast to commutative, free and Boolean cases. We have succeeded in clarifying it…

We prove Terao conjecture saying that the freeness is determined by the combinatorics for arrangements of 13 lines in the complex projective plane and that the property of being nearly free is combinatorial for line arrangements of up to 12…

For a convergence group equipped with an expanding coarse-cocycle, we construct finitely generated free subsemigroups, which we call $\textit{Bishop--Jones}$ $\textit{semigroups}$, of critical exponent arbitrarily close to but strictly less…

Let $(Q,\mathfrak n,k)$ be a commutative local Noetherian ring, $f_1,\dots, f_c$ a $Q$-regular sequence in $\mathfrak n$, and $R=Q/(f_1,\dots,f_c)$. Given a complex of finitely generated free $R$-modules, we give a construction of a complex…

Let $(\A, \alpha)$ and $(\B, \beta)$ be C*-dynamical systems and assume that $\A$ is a separable simple C*-algebra and that $\alpha$ and $\beta$ are *-automorphisms. Then the semicrossed products $\A \times_{\alpha} \bbZ^{+}$ and $\B…