Conformal cochains

Wilson, Scott

doi:10.1090/S0002-9947-08-04556-X

Conformal cochains

Author: Scott O. Wilson
Journal: Trans. Amer. Math. Soc. 360 (2008), 5247-5264
MSC (2000): Primary 57R57, 32G20; Secondary 30F99
DOI: https://doi.org/10.1090/S0002-9947-08-04556-X
Published electronically: April 10, 2008
Addendum: Trans. Amer. Math. Soc. 365 (2013), 5033-5033.
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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