Author:
Cornelissen Gunther,Peyerimhoff Norbert
Abstract
AbstractIn this chapter, we collect some information on various constructions of manifolds, orbifolds, and their covers. Notably, we discuss the notions of fiber product (in the sense of Thurston) and compositum of manifolds over a common developable orbifold, the difference with the set-theoretic fiber product, the connected components of the fiber product, compositum of Galois covers, normal closure of a cover, and the relation between commensurability, arithmeticity, and the existence of certain covers in relation to Mostow rigidity.
Publisher
Springer International Publishing
Reference13 articles.
1. Sheng Chen, Constructing isospectral but nonisometric Riemannian manifolds, Canad. Math. Bull. 35 (1992), no. 3, 303–310.
2. Suhyoung Choi, Geometric structures on 2-orbifolds: exploration of discrete symmetry, MSJ Memoirs, vol. 27, Mathematical Society of Japan, Tokyo, 2012.
3. Michael W. Davis and John W. Morgan, Finite group actions on homotopy 3-spheres, in: The Smith conjecture (New York, 1979; J.W. Morgan and H. Bass, eds.), Pure Appl. Math., vol. 112, Academic Press, Orlando, FL, 1984, pp. 181–225.
4. Benjamin Linowitz, David B. McReynolds, Paul Pollack, and Lola Thompson, Counting and effective rigidity in algebra and geometry, Invent. Math. 213 (2018), no. 2, 697–758.
5. Alexander Lubotzky, Beth Samuels, and Uzi Vishne, Division algebras and noncommensurable isospectral manifolds, Duke Math. J. 135 (2006), no. 2, 361–379.