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University of Cambridge > Talks.cam > Geometric Group Theory (GGT) Seminar > The taut spectrum and the Eilenberg-Ganea problem

## The taut spectrum and the Eilenberg-Ganea problemAdd to your list(s) Download to your calendar using vCal - Luis Jorge Sanchez Saldana (UNAM)
- Friday 15 October 2021, 13:45-14:45
- Zoom https://maths-cam-ac-uk.zoom.us/j/95208706709.
If you have a question about this talk, please contact . A well-known open problem in group theory is the existence of a group with cohomological dimension 2 and geometric dimension 3, known as the Eilenberg-Ganea problem. For relative versions of this problem there are examples of groups with relative cohomological dimension 2 and relative geometric dimension 3 due to the work of several authors. We call the aforementioned groups relative Eilenberg-Ganea groups. On the other hand, in geometric group theory, it is usual to try to classify groups up to quasi-isometry. In this talk we will explore roughly how many non quasi-isometric groups are among the class of relative Eilenberg-Ganea groups. Explicitly, using a quasi-isometry invariant introduced by Bowditch, called the Taut spectrum, we will sketch how to prove that there are continuously many non-quasi-isometric groups with proper (resp. virtually cyclic) cohomological dimension 2 and proper (resp. virtually cyclic) geometric dimension 3. This is joint work with Eduardo MartÃnez-Pedroza. This talk is part of the Geometric Group Theory (GGT) Seminar series. ## This talk is included in these lists:- All CMS events
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