376 research outputs found
Natural Stratifications of Reeb Spaces and Higher Morse Functions
Both Reeb spaces and higher Morse functions induce natural stratifications.
In the former, we show that the data of the Jacobi set of a function induces stratifications on , and the associated
Reeb space, and give conditions under which maps between these three spaces are
stratified maps. We then extend this type of construction to the codomain of
higher Morse functions, using the singular locus to induce a stratification of
which sub-posets are equivalent to multi-parameter filtrations.Comment: v2: Additional examples/figures, Appendix on notions of criticality
for PL ma
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