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TRHW02 | Mr. Csaba Nagy | Homotopy equivalence and simple homotopy equivalence of manifolds
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TRHW02 | Mr. Csaba Nagy | Homotopy equivalence and simple homotopy equivalence of manifolds
Speaker: Mr Csaba Nagy (University of Glasgow)
Date: 17th Jun 2024 - 13:45 to 14:15
Venue: External
Title: Homotopy equivalence and simple homotopy equivalence of manifolds
Event: (TRHW02) International Conference
Abstract: 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.
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The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.
Speaker: Mr Csaba Nagy (University of Glasgow)
Date: 17th Jun 2024 - 13:45 to 14:15
Venue: External
Title: Homotopy equivalence and simple homotopy equivalence of manifolds
Event: (TRHW02) International Conference
Abstract: 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.
👉 Want to learn more about the talks in this stream?
-------------------
FOLLOW US
SEMINAR ROOMS
ABOUT
The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.