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Homotopy equivalence and simple homotopy equivalence of manifolds

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  • UserCsaba Nagy (University of Glasgow)
  • ClockMonday 17 June 2024, 13:45-14:15
  • HouseExternal.

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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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Rooms SG1 & SG2, Alison Richard Building, 7 West Road, Cambridge, CB3 9DT Average on weekdays: 9023.39808917 kWh Seminar time is 1pm BST in Room FW 11, Willam Gates Hall. Zoom link: https://cl-cam-ac-uk.zoom.us/j/4361570789?pwd=Nkl2T3ZLaTZwRm05bzRTOUUxY3Q4QT09&from=addon

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