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

Ye, Shengkui¹

¹Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, UK

Algebraic and Geometric Topology, Tome 13 (2013) no. 5, pp. 2947-2965

Résumé

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

Détail

DOI : 10.2140/agt.2013.13.2947

Classification : 57N15, 19D06, 14F35, 58J50
Keywords: Quillen's plus construction, homology spheres, homology equivalences, $G$–dense rings, zero-in-the spectrum conjecture

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