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Number Theory, Analysis and Geometry pp 161–168Cite as

Harmonic representatives for cuspidal cohomology classes

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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.

Mathematics Subject Classification (2010): 30F30, 58J60

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References

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Authors and Affiliations

  1. PHD Program in Mathematics, Grad School and University Center (CUNY), 365 5th Avenue, New York, NY, 10016-4309, USA

    Józef Dodziuk

  2. Department of Mathematical Sciences, Central Connecticut State University, 1615 Stanley Street, New Britain, CT, 06050, USA

    Jeffrey McGowan

  3. Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY, 40506-0027, USA

    Peter Perry

Authors
  1. Józef Dodziuk
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  2. Jeffrey McGowan
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  3. Peter Perry
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Corresponding author

Correspondence to Józef Dodziuk .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Columbia University, Broadway 2990, New York, 10027, New York, USA

    Dorian Goldfeld

  2. , Department of Mathematics, City College of New York, New York, 10031, New York, USA

    Jay Jorgenson

  3. , Department of Mathematics, Yale University, Hillhouse Ave. 10, New Haven, 06520, Connecticut, USA

    Peter Jones

  4. , Department of Mathematics, California Institute of Technology, E. California Blvd. 1200, Pasadena, 91125, California, USA

    Dinakar Ramakrishnan

  5. , Department of Mathematics, University of California at Berkeley, Evans Hall 925, Berkeley, 94720-3840, California, USA

    Kenneth Ribet

  6. , Department of Mathematics, Harvard University, Science Center/One Oxford Street, Cambridge, 02138, Massachusetts, USA

    John Tate

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Dedicated to the memory of Serge Lang

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Dodziuk, J., McGowan, J., Perry, P. (2012). Harmonic representatives for cuspidal cohomology classes. In: Goldfeld, D., Jorgenson, J., Jones, P., Ramakrishnan, D., Ribet, K., Tate, J. (eds) Number Theory, Analysis and Geometry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1260-1_8

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