Search results for "Regular homotopy"

A note on conjugation involutions on homotopy complex projective spaces

1986

Introduction to Homotopy Theory

2001

Consider two manifolds X and Y together with a set of continuous maps f, g,... $$ f:X \to Y,x \to f(x) = y;x \in X,y \in Y. $$

Data structures and algorithms for topological analysis

2014

International audience; One of the steps of geometric modeling is to know the topology and/or the geometry of the objects considered. This paper presents different data structures and algorithms used in this study. We are particularly interested by algebraic structures, eg homotopy and homology groups, the Betti numbers, the Euler characteristic, or the Morse-Smale complex. We have to be able to compute these data structures, and for (homotopy and homology) groups, we also want to compute their generators. We are also interested in algorithms CIA and HIA presented in the thesis of Nicolas DELANOUE, which respectively compute the connected components and the homotopy type of a set defined by…

On the proper homotopy invariance of the Tucker property

2006

A non-compact polyhedron P is Tucker if, for any compact subset K ⊂ P, the fundamental group π1(P − K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru’s theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map.

Discrete and differential homotopy in circular restricted three-body control

2010

The planar circular restricted three-body problem is considered. The control enters linearly in the equation of motion to model the thrust of the third body. The minimum time optimal control problem has two scalar parameters: The ratio of the primaries masses which embeds the two-body problem into the three-body one, and the upper bound on the control norm. Regular extremals of the maximum principle are computed by shooting thanks to continuations with respect to both parameters. Discrete and dierential homotopy are compared in connection with second order sucient conditions in optimal control. Homotopy with respect to control bound gives evidence of various topological structures of extr…