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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Conformal cochains


Author: Scott O. Wilson
Journal: Trans. Amer. Math. Soc. 360 (2008), 5247-5264
MSC (2000): Primary 57R57, 32G20; Secondary 30F99
Published electronically: April 10, 2008
Addendum: Tran. Amer. Math. Soc. 365 (2013), 5033-5034
MathSciNet review: 2415073
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Abstract: In this paper we define holomorphic cochains and an associated period matrix for triangulated closed topological surfaces. We use the combinatorial Hodge star operator introduced in the author's paper of 2007, which depends on the choice of an inner product on the simplicial 1-cochains.

We prove that for a triangulated Riemannian 2-manifold (or a Riemann surface), and a particularly nice choice of inner product, the combinatorial period matrix converges to the (conformal) Riemann period matrix as the mesh of the triangulation tends to zero.


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Additional Information

Scott O. Wilson
Affiliation: School of Mathematics, University of Minnesota-Twin Cities, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, Minnesota 55455
Email: scottw@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04556-X
PII: S 0002-9947(08)04556-X
Keywords: Cochains, Hodge-star, Riemann surface, period matrices
Received by editor(s): August 8, 2006
Published electronically: April 10, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.