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Given a compact smooth manifold $M$ with non-empty boundary and a Morse function, a pseudo-gradient Morse-Smale vector field adapted to the boundary allows one to build a Morse complex whose homology is isomorphic to the (absolute or relative to the boundary) homology of $M$ with integer coefficients. Our approach simplifies other methods which have been discussed in more specific geometric settings.
Combinatorial Ricci flow on an ideally triangulated compact 3-manifold with boundary was introduced by Luo as a 3-dimensional analog of Chow-Luos combinatorial Ricci flow on a triangulated surface and conjectured to find algorithmically the complete
This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from cite{GrLaPo}, cite{GrLaPo1}, where gradient-like case was considered. We introduce a kind of Morse-Lyapunov function, called dynamically ordered, which f
To every Gromov hyperbolic space X one can associate a space at infinity called the Gromov boundary of X. Gromov showed that quasi-isometries of hyperbolic metric spaces induce homeomorphisms on their boundaries, thus giving rise to a well-defined no
We build an analogue of the Gromov boundary for any proper geodesic metric space, hence for any finitely generated group. More precisely, for any proper geodesic metric space $X$ and any sublinear function $kappa$, we construct a boundary for $X$, de
Let $M$ be a smooth manifold and let $F$ be a codimension one, $C^infty$ foliation on $M$, with isolated singularities of Morse type. The study and classification of pairs $(M,F)$ is a challenging (and difficult) problem. In this setting, a classical