Homotopy equivalence and simple homotopy equivalence of manifolds

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• Csaba Nagy (University of Glasgow)
• Monday 17 June 2024, 13:45-14:15
• External.

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TRHW02 - International Conference

A homotopy equivalence between finite CW-complexes is called simple if it is homotopic to a composition of elementary collapses and expansions. Lens spaces provide famous examples of manifolds that are homotopy equivalent but not simple homotopy equivalent to each other, in all $\geq 3$ odd dimensions. However, no even-dimensional examples are known in the literature. We construct even-dimensional manifolds that are homotopy equivalent (in fact h-cobordant) but not simple homotopy equivalent to each other. More generally, we give a purely algebraic characterisation of groups G with the property that there exists a pair of manifolds with fundamental group G that are h-cobordant but not simple homotopy equivalent. This is joint work with Johnny Nicholson and Mark Powell.

This talk is part of the Isaac Newton Institute Seminar Series series.

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