Morse Inequalities for Orbifold Cohomology
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Morse Inequalities for Orbifold Cohomology. / A. Hepworth, Richard.
In: Algebraic & Geometric Topology, Vol. 9, No. 2, 2009, p. 1105-1175.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Morse Inequalities for Orbifold Cohomology
AU - A. Hepworth, Richard
N1 - Keywords: math.AT; math.GT; 57R70, 57N65
PY - 2009
Y1 - 2009
N2 - This paper begins the study of Morse theory for orbifolds, or more precisely 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.
AB - This paper begins the study of Morse theory for orbifolds, or more precisely 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.
U2 - 10.2140/agt.2009.9.1105
DO - 10.2140/agt.2009.9.1105
M3 - Journal article
VL - 9
SP - 1105
EP - 1175
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 2
ER -
ID: 21543291