Algebra seminar - Coherence, non-positive immersions and L^2-Betti numbers
| Dates: | 10 October 2023 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Marco Linton |
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Abstract: A group is said to be coherent if all of its finitely generated subgroups are finitely presented. Proving a group or a class of groups is coherent can often be a delicate task since many seemingly innocuous groups turn out to not be coherent, the prototypical example being the direct product of two non-abelian free groups. In this talk, I will discuss connections between coherence, the non-positive immersions property and the vanishing of the second L^2-Betti number. I will then show how these connections lead to a proof that all one-relator groups are coherent, solving an old problem of Baumslag's. Joint work with Andrei Jaikin-Zapirain.
Speaker
Marco Linton
Organisation: University of Oxford
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Frank Adams 1
Alan Turing Building
Manchester
