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Stable Commutator Length

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  • UserNicolaus Heuer (Oxford)
  • ClockFriday 16 November 2018, 15:00-16:00
  • HouseMR13.

If you have a question about this talk, please contact Ben Morley.

Given a loop $\gamma$ in a topological space $X$. What is complexity of the surfaces needed to bound $\gamma$? This question may answered using the stable commutator length (scl) of $[\gamma] \in \pi_1(X)$. This invariant of group elements has many intriguing algebraic, geometric and analytic features.

I will introduce and motivate the theory of scl by giving highlight theorems and – most importantly – many open problems.

Finally, I will discuss a relation between scl in free groups and the l1-homology of one-relator groups. This is joint work with Clara Löh.

This talk is part of the Junior Geometry Seminar series.

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