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Crystallizations of generalized lens spaces

Basudeb Datta

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 $S^{2n+1}$.

Crystallizations of generalized lens spaces

Abstract

We present some natural crystallizations of the generalized lens spaces for integers , and integers relatively prime to . These crystallizations are quotients of triangulations of the sphere .
Paper Structure (3 sections, 5 theorems, 9 equations)

This paper contains 3 sections, 5 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Constructions of Crystallizations

Key Result

Proposition 2.1

Let $X$ be a simplicial cell complex, and let $G \leq \operatorname{Aut}(X)$. The quotient poset $X/G$ is a simplicial cell complex if and only if the action of $G$ on $X$ is good.

Theorems & Definitions (8)

  • Proposition 2.1
  • Proposition 2.2
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Theorem 3.3
  • proof