Harmonic representatives for cuspidal cohomology classes

Józef Dodziuk; Jeffrey McGowan; Peter Perry

doi:10.1007/978-1-4614-1260-1_8

Harmonic representatives for cuspidal cohomology classes

Józef Dodziuk
, Jeffrey McGowan
, Peter Perry

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

We give a construction of harmonic differentials that uniquely represent cohomology classes of a non-compact Riemann surface of finite topology. We construct these differentials by cutting off all cusps along horocycles and solving a suitable boundary value problem on the truncated surface. We then pass to the limit as the horocycle in each cusp recedes to infinity.

Original language	English
Title of host publication	Number Theory, Analysis and Geometry
Subtitle of host publication	In Memory of Serge Lang
Pages	161-168
Number of pages	8
Volume	9781461412601
ISBN (Electronic)	9781461412601
DOIs	https://doi.org/10.1007/978-1-4614-1260-1_8
State	Published - Mar 1 2012

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media, LLC 2012. All rights reserved.

Keywords

harmonic differentials
non-compact Riemann surfaces

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-1-4614-1260-1_8

Cite this

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AB - We give a construction of harmonic differentials that uniquely represent cohomology classes of a non-compact Riemann surface of finite topology. We construct these differentials by cutting off all cusps along horocycles and solving a suitable boundary value problem on the truncated surface. We then pass to the limit as the horocycle in each cusp recedes to infinity.

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KW - non-compact Riemann surfaces

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Harmonic representatives for cuspidal cohomology classes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this