Abstract
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 –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.
Citation
Shengkui Ye. "Homology equivalences of manifolds and zero-in-the-spectrum examples." Algebr. Geom. Topol. 13 (5) 2947 - 2965, 2013. https://doi.org/10.2140/agt.2013.13.2947
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