A Morse complex on manifolds with boundary

Francois Laudenbach (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: Morse theory; pseudo-gradient

Domaines: Topologie géométrique [math.GT]

Francois Laudenbach. A Morse complex on manifolds with boundary. Geometriae Dedicata, 2011, 1 (153), pp.47 - 57. ⟨hal-00466294v2⟩