相关论文: The space of discrete Morse functions

It turns out that complex geodesics in Teichm\"uller spaces with respect to their invariant metrics are intrinsically connected with variational calculus for univalent functions. We describe this connection and show how geometric features…

We present a brief review of discrete structures in a finite Hilbert space, relevant for the theory of quantum information. Unitary operator bases, mutually unbiased bases, Clifford group and stabilizer states, discrete Wigner function,…

In this paper we make two observations related to discrete torsion. First, we observe that an old obscure degree of freedom (momentum/translation shifts) in (symmetric) string orbifolds is related to discrete torsion. We point out how our…

We introduce and study (metrically) quarter-stratifiable spaces and then apply them to generalize Rudin and Kuratowski-Montgomery theorems about the Baire and Borel complexity of separately continuous functions.

We denote the matching complex of the complete graph with $n$ vertices by $M_n$. Bouc first studied the topological properties of $M_n$ in connection with the Quillen complex. Later Bj\"{o}rner, Lov\'{a}sz, Vre\'{c}ica, and…

Given a simplicial complex $K$ and an injective function $f$ from the vertices of $K$ to $\mathbb{R}$, we consider algorithms that extend $f$ to a discrete Morse function on $K$. We show that an algorithm of King, Knudson and Mramor can be…

In the context of discrete Morse theory, we introduce Morse frames, which are maps that associate a set of critical simplexes to all simplexes. The main example of Morse frames are the Morse references. In particular, these Morse references…

We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type…

Many fundamental structures of Riemannian geometry have found discrete counterparts for graphs or combinatorial ones for simplicial complexes. These include those discussed in this survey, Hodge theory, Morse theory, the spectral theory of…

We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computationally tractable description of the bounded derived category…

We introduce filtrations in chiral homology complexes of smooth elliptic curves, exploiting the mixed Hodge structure on cohomology groups of configuration spaces. We use these to relate the chiral homology of a smooth elliptic curve with…

In this paper, new classes of functions are defined. These spaces generalize Morrey spaces and give a refinement of Lebesgue spaces. Some embeddings between these new classes are also proved. Finally, the authors apply these classes of…

We prove that the complement of a toric arrangement has the homotopy type of a minimal CW complex. As a corollary we obtain that the integer cohomology of these spaces is torsion free. We use Discrete Morse Theory, providing a sequence of…

The spaces of directed paths on the geometric realizations of pre-cubical sets, called also $\square$--sets, can be interpreted as the spaces of possible executions of Higher Dimensional Automata, which are models for concurrent…

We derive properties and a characterization of discrete composition matrices which are useful in the field of numerical computation of shape correspondences.

We develop a theory of abstract intermediate function spaces on a compact convex set $X$ and study the behaviour of multipliers and centers of these spaces. In particular, we provide some criteria for coincidence of the center with the…

Persistent Homology (PH) allows tracking homology features like loops, holes and their higher-dimensional analogs, along with a single-parameter family of nested spaces. Currently, computing descriptors for complex data characterized by…

We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…

Our objective is to develop a stratified Morse theory with tangential conditions. We define a continuous strata-wise smooth Morse function on an abstract stratified space by using control conditions and radiality assumptions on the gradient…

In this article, we define discrete analogue of generalized Hardy spaces and its separable subspace on a homogenous rooted tree and study some of its properties such as completeness, inclusion relations with other spaces, separability,…