Morse Inequalities for Orbifold Cohomology

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

SN - 1472-2747

VL - 9

SP - 1105

EP - 1175

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 2

ER -