Crystallizations of generalized lens spaces

TL;DR

This paper introduces natural crystallizations of generalized lens spaces as quotients of sphere triangulations, expanding the understanding of their combinatorial structures.

Contribution

It provides explicit crystallizations of generalized lens spaces derived from sphere triangulations, offering new combinatorial models for these manifolds.

Findings

Crystallizations are constructed as quotients of sphere triangulations.

The approach applies to a broad class of generalized lens spaces.

Provides a combinatorial perspective on lens space topology.

Abstract

We present some natural crystallizations of the generalized lens spaces $L(p, q_1, \dots, q_n)$ for integers $p\geq 2$, $n\geq 1$ and integers $q_1, \dots, q_n$ relatively prime to $p$. These crystallizations are quotients of triangulations of the sphere $S^{2n+1}$.