Morse Inequalities for Orbifold Cohomology

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Morse Inequalities for Orbifold Cohomology. / A. Hepworth, Richard.

I: Algebraic & Geometric Topology, Bind 9, Nr. 2, 2009, s. 1105-1175.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

A. Hepworth, R 2009, 'Morse Inequalities for Orbifold Cohomology', Algebraic & Geometric Topology, bind 9, nr. 2, s. 1105-1175. https://doi.org/10.2140/agt.2009.9.1105

APA

A. Hepworth, R. (2009). Morse Inequalities for Orbifold Cohomology. Algebraic & Geometric Topology, 9(2), 1105-1175. https://doi.org/10.2140/agt.2009.9.1105

Vancouver

A. Hepworth R. Morse Inequalities for Orbifold Cohomology. Algebraic & Geometric Topology. 2009;9(2):1105-1175. https://doi.org/10.2140/agt.2009.9.1105

Author

A. Hepworth, Richard. / Morse Inequalities for Orbifold Cohomology. I: Algebraic & Geometric Topology. 2009 ; Bind 9, Nr. 2. s. 1105-1175.

Bibtex

@article{d34bb590af4611df825b000ea68e967b,
title = "Morse Inequalities for Orbifold Cohomology",
abstract = "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.",
author = "{A. Hepworth}, Richard",
note = "Keywords: math.AT; math.GT; 57R70, 57N65",
year = "2009",
doi = "10.2140/agt.2009.9.1105",
language = "English",
volume = "9",
pages = "1105--1175",
journal = "Algebraic and Geometric Topology",
issn = "1472-2747",
publisher = "Geometry & Topology Publications",
number = "2",

}

RIS

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