Homology equivalences of manifolds and zero-in-the-spectrum examples

Abstract

Working with group homomorphisms, a construction of manifolds is introduced to preserve homology groups. The construction gives as special cases Qullien's plus construction with handles obtained by Hausmann, the existence of one-sided $h$-cobordism of Guilbault and Tinsley, the existence of homology spheres and higher-dimensional knots proved by Karvaire. We also use it to get counter-examples to the zero-in-the-spectrum conjecture found by Farber-Weinberger, and by Higson-Roe-Schick.

some typos are corrected. Final version, to appear in Algebraic & Geometric Topology

References in corpus (2)

• Spaces with vanishing $l\sp 2$-homology and their fundamental groups (after Farber and Weinberger)
• Spherical alterations of handles: embedding the manifold plus construction

Cited by in corpus (1)

• Fundamental groups, homology equivalences and one-sided h-cobordisms