A Morse complex on manifolds with boundary

Details A Morse complex on manifolds with boundary A Morse complex on manifolds with boundary

2010-03-26

arxiv.org/abs/1003.5077v2

Geometriae Dedicata 1, 153 (2011) 47 - 57

Mathematics

Geometric Topology

Scientific paper

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.

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