University of Birmingham > Talks@bham > Groups St Andrews 2017 > On ℓ^2-Betti numbers and their analogues in positive characteristic

## On ℓ^2-Betti numbers and their analogues in positive characteristicAdd to your list(s) Download to your calendar using vCal - Andrei Jaikin-Zapirain, Universidad Autónoma de Madrid
- Saturday 12 August 2017, 09:30-10:30
- Poynting Physics, Large Lecture Theatre.
If you have a question about this talk, please contact David Craven. Let G > _{2}G > ··· be a chain of normal subgroups of _{3}G of finite index with trivial intersection. The multiplication on the right side by A induces linear mapsφ ^{n} → K[G/G]_{i}^{m}
( v_{1},...,v) → (_{n}v_{1},...,v)_{n}A.We are interested in properties of the sequence {dim G:G|}. In particular, we would like to answer the following questions._{i}- Is there the limit lim
_{i → ∞}dim_{K}ker φ/ |_{i}*G*:*G*|?_{i} - If the limit exists, how does it depend on the chain {
*G*}?_{i} - What is the range of possible values for lim
_{i → ∞}dim_{K}ker φ/ |_{i}*G*:*G*| for a given group_{i}*G*?
It turns out that the answers on these questions are known for many groups This talk is part of the Groups St Andrews 2017 series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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