Related papers: Singularity Collisions through Homotopical Dynamic…

In this article, we present a dynamical homotopical cancellation theory for Gutierrez-Sotomayor singular flows $\varphi$, GS-flows, on singular surfaces $M$. This theory generalizes the classical theory of Morse complexes of smooth…

We investigate combinatorial dynamical systems on simplicial complexes considered as {\em finite topological spaces}. Such systems arise in a natural way from sampling dynamics and may be used to reconstruct some features of the dynamics…

This paper is a survey of the generalized Hamiltonian gradient flow (GHGF) framework for Hamilton-Jacobi equations, with an emphasis on the propagation of singularities and its connections to weak KAM theory, optimal transport and mean…

We show how the coupling of gravitinos and gauginos to fluxes modifies anomaly cancellation in M-theory on a manifold with boundary. Anomaly cancellation continues to hold, after a shift of the definition of the gauge currents by a local…

We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the…

In this work we address the realizability of a Lyapunov graph labeled with GS singularities, namely regular, cone, Whitney, double crossing and triple crossing singularities, as continuous flow on a singular closed $2$-manifold…

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…

Given a smooth closed manifold M, the Morse-Witten complex associated to a Morse function f and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines…

Discrete Morse theory helps us compute the homology groups of simplicial complexes in an efficient manner. A "good" gradient vector field reduces the number of critical simplices, simplifying the homology calculations by reducing them to…

Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered,…

The purpose of this work is to develop a version of Forman's discrete Morse theory for simplicial complexes, based on internal strong collapses. Classical discrete Morse theory can be viewed as a generalization of Whitehead's collapses,…

We try to convince the reader that the categorical version of differential geometry, called Synthetic Differential Geometry (SDG), offers valuable tools which can be applied to work with some unsolved problems of general relativity. We do…

In this paper, we develop the notion of a Morse sequence, which provides an alternative approach to discrete Morse theory, and which is both simple and effective. A Morse sequence on a finite simplicial complex is a sequence composed solely…

We pursue the analogy of a framed flow category with the flow data of a Morse function. In classical Morse theory, Morse functions can sometimes be locally altered and simplified by the Morse moves. These moves include the Whitney trick…

Globular complexes were introduced by E. Goubault and the author in arXiv:math/0107060 to model higher dimensional automata. Globular complexes are topological spaces equipped with a globular decomposition which is the directed analogue of…

We construct a Floer type boundary operator for generalised Morse-Smale dynamical systems on compact smooth manifolds by counting the number of suitable flow lines between closed (both homoclinic and periodic) orbits and isolated critical…

An explicit isomorphism between Morse homology and singular homology is constructed via the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a Morse function, the unstable manifolds for the negative…

This work addresses the response of a holographic conformal field theory to a homogeneous gravitational periodic driving. The dual geometry is the AdS-soliton, which models a strongly coupled quantum system in a gapped phase, on a compact…

We define a notion of equivariant non-degeneracy of $G$-maps to introduce the class of equivariantly non-degenerate flows on smooth compact manifolds with compact Lie group action. We prove genericity of this class and use this result to…

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…