On Calabi-Yau threefolds with large nonabelian fundamental groups

TL;DR

This paper constructs specific Calabi-Yau threefolds with large nonabelian fundamental groups, expanding the understanding of their topological properties through quotient constructions of known complete intersections.

Contribution

It introduces a method to produce Calabi-Yau threefolds with nonabelian fundamental groups of order 64 via quotients of complete intersections in projective space.

Findings

Constructed Calabi-Yau threefolds with fundamental group of order 64

Demonstrated quotient construction from complete intersections

Extended known examples of Calabi-Yau topologies

Abstract

In this short note we construct Calabi-Yau threefolds with nonabelian fundamental groups of order 64 as quotients of the small resolutions of certain complete intersections of quadrics in $\PP^7$ that were first considered by M. Gross and S. Popescu.