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Harmonic representatives for cuspidal cohomology classes

In: Number Theory, Analysis and Geometry

Author

Listed:
  • Józef Dodziuk

    (Grad School and University Center (CUNY), PHD Program in Mathematics)

  • Jeffrey McGowan

    (Central Connecticut State University, Department of Mathematical Sciences)

  • Peter Perry

    (University of Kentucky, Department of Mathematics)

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.

Suggested Citation

  • Józef Dodziuk & Jeffrey McGowan & Peter Perry, 2012. "Harmonic representatives for cuspidal cohomology classes," Springer Books, in: Dorian Goldfeld & Jay Jorgenson & Peter Jones & Dinakar Ramakrishnan & Kenneth Ribet & John Tate (ed.), Number Theory, Analysis and Geometry, edition 127, pages 161-168, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-1260-1_8
    DOI: 10.1007/978-1-4614-1260-1_8
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