Vol. 2, No. 1, 2020

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Looijenga line bundles in complex analytic elliptic cohomology

Charles Rezk

Vol. 2 (2020), No. 1, 1–42

We present a calculation that shows how the moduli of complex analytic elliptic curves arises naturally from the Borel cohomology of an extended moduli space of U(1)-bundles on a torus. Furthermore, we show how the analogous calculation, applied to a moduli space of principal bundles for a K(,2) central extension of U(1)d, gives rise to Looijenga line bundles. We then speculate on the relation of these calculations to the construction of complex analytic equivariant elliptic cohomology.

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elliptic cohomology, Looijenga line bundle
Mathematical Subject Classification 2010
Primary: 55N34
Secondary: 55N91, 55R40
Received: 26 February 2018
Revised: 4 August 2018
Accepted: 19 August 2018
Published: 22 March 2019
Charles Rezk
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801
United States