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

Shengkui Ye

doi:10.2140/agt.2013.13.2947

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arXiv · 1301.6233

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

Shengkui Ye

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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.

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Shengkui Ye. 2013-05-04. Homology equivalences of manifolds and zero-in-the-spectrum examples. https://doi.org/10.2140/agt.2013.13.2947

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