Stable commutator length in subgroups of PL(I)
Danny Calegari
TL;DR
This paper proves that in any subgroup of PL(I), the stable commutator length of elements in the commutator subgroup is always zero, revealing a specific algebraic property of these groups.
Contribution
It establishes that all elements in the commutator subgroup of any subgroup of PL(I) have zero stable commutator length, a new result in geometric group theory.
Findings
Stable commutator length of elements in [G,G] is zero for subgroups of PL(I)
Provides insight into the algebraic structure of subgroups of PL(I)
Advances understanding of commutator properties in piecewise linear groups
Abstract
Let G be a subgroup of PL(I). Then the stable commutator length of every element of [G,G] is zero.
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Advanced Algebra and Geometry