Floer homology for negative line bundles and Reeb chords in prequantization spaces

Peter Albers; Urs Frauenfelder

doi:10.3934/jmd.2009.3.407

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2009, Volume 3, Issue 3: 407-456. Doi: 10.3934/jmd.2009.3.407

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Floer homology for negative line bundles and Reeb chords in prequantization spaces

Peter Albers^1, and
Urs Frauenfelder^2,

1.
Purdue University, Department of Mathematics, 150 N. University Street, West Lafayette, IN 47907-2067
2.
Department of Mathematics and Research Institute of Mathematics, Seoul National University

Received: November 30, 2008

Revised: June 30, 2009

Published: July 2009

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Abstract

We prove existence of Reeb orbits for Bohr - Sommerfeld Legendrians in certain prequantization spaces. We give a quantitative estimate from below. These estimates are obtained by studying Floer homology for fiberwise quadratic Hamiltonian functions on negative line bundles.

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Mathematics Subject Classification: Primary: 53D40, 53D12; Secondary: 37J99.

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