On stratified Morse theory: from topology to constructible sheaves

Journal of Singularities
volume 13 (2015), 141-158

Received 4 September 2013. Received in revised form 9 January 2015.

DOI: 10.5427/jsing.2015.13g

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Abstract:

Stratified Morse theory is the generalization of usual Morse theory to functions on stratified spaces. There are versions for the topological type, homotopy type or (co)homology. A standard reference is the book of Goresky-MacPherson which primarily treats the topological type. Corresponding results about the homotopy type or cohomology may be expected to be consequences but in fact usually one needs some extra information, in particular in the case of cohomology of constructible sheaves, as we will see in this paper.

Keywords:

Morse theory, stratification, constructible sheaf

Mathematical Subject Classification:

32S60, 58K05

Author(s) information:

Helmut A. Hamm
Mathematisches Institut der WWU
Einsteinstr. 62
48149 Münster, Germany
email: hamm@uni-muenster.de