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This paper begins the study of Morse theory for orbifolds, or equivalently for differentiable Deligne–Mumford stacks. The main result is an analogue of the Morse inequalities that relates the orbifold Betti numbers of an almost-complex orbifold to the critical points of a Morse function on the orbifold. We also show that a generic function on an orbifold is Morse. In obtaining these results we develop for differentiable Deligne–Mumford stacks those tools of differential geometry and topology—flows of vector fields, the strong topology—that are essential to the development of Morse theory on manifolds.
Hepworth, Richard 1
@article{10_2140_agt_2009_9_1105,
author = {Hepworth, Richard},
title = {Morse inequalities for orbifold cohomology},
journal = {Algebraic and Geometric Topology},
pages = {1105--1175},
publisher = {mathdoc},
volume = {9},
number = {2},
year = {2009},
doi = {10.2140/agt.2009.9.1105},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.1105/}
}
TY - JOUR AU - Hepworth, Richard TI - Morse inequalities for orbifold cohomology JO - Algebraic and Geometric Topology PY - 2009 SP - 1105 EP - 1175 VL - 9 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2009.9.1105/ DO - 10.2140/agt.2009.9.1105 ID - 10_2140_agt_2009_9_1105 ER -
Hepworth, Richard. Morse inequalities for orbifold cohomology. Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 1105-1175. doi: 10.2140/agt.2009.9.1105
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