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Calabi–Yau threefold; torsion; cocompact lattice; unitary representation

We prove that there are cocompact lattices $\Gamma$ in $\rm SL(2,\mathbb C)$ with the property that there are holomorphic line bundles $L$ on $\rm SL(2,\mathbb C)/ \Gamma$ with $c_{1}(L) = 0$ such that $L$ does not admit any unitary flat connection.

INDRANIL BISWAS¹ GEORG SCHUMACHER²

1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
2. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Lahnberge, Hans-Meerwein-Strasse, D-35032 Marburg, Germany

Published

1 June 2017

Manuscript received

27 October 2016

Manuscript revised

Accepted

6 December 2016

Early published

Unedited version published online

Final version published online

1 June 2017