3 results
On stable commutator length of non-filling curves in surfaces
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 14 December 2023, pp. 1-18
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We give a new proof of rationality of stable commutator length (scl) of certain elements in surface groups: those represented by curves that do not fill the surface. Such elements always admit extremal surfaces for scl. These results also hold more generally for non-filling $1$
–chains.
Commutator length of powers in free products of groups
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 1 / February 2022
- Published online by Cambridge University Press:
- 27 December 2021, pp. 102-119
-
- Article
- Export citation
-
Given groups $A$
and $B$
, what is the minimal commutator length of the 2020th (for instance) power of an element $g\in A*B$
not conjugate to elements of the free factors? The exhaustive answer to this question is still unknown, but we can give an almost answer: this minimum is one of two numbers (simply depending on $A$
and $B$
). Other similar problems are also considered.
Surface groups, infinite generating sets, and stable commutator length
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 5 / October 2020
- Published online by Cambridge University Press:
- 23 April 2019, pp. 2379-2386
- Print publication:
- October 2020
-
- Article
- Export citation
