Stable commutator length in graphs of groupsmath.uchicago.edu/~lzchen/slides/sclBS_talk.pdf · in graphs of groups NCNGT 1 Lvzhou Chen NCNGT May 27, 2020. LvzhouChen NCNGT 2 Stable

Lvzhou Chen

Stable commutator length

in graphs of groups

NCNGT 1

Lvzhou Chen

NCNGT

May 27, 2020

Lvzhou Chen NCNGT 2

Stable commutator length (scl)

Definition

Admissible surfaces2

2

1

1

Multiplicative!

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Stable commutator length (scl)

Definition

Example

Challenge: prove lower bounds of scl or compute it.

Admissible surfaces

Space of surfaces has little structure.

Multiplicative!

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Properties

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Gromov–Thurston norm

Remove “embedded” by Gabai–Thurston

Gromov Norm

Example

extremal

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Extremal surfaces

Definition

Note: extremalfinite cover

extremal

Proof: Compression+LERF

Proposition

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Computations and rationality

Theorem (Calegari’08)

Gromov’s Question

Application (surface subgroups)

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Main theorem

Theorem (C.’19)

Examples

f.i

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Proof ideas

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Relative admissible surfaces

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Simple normal form

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Simple normal form

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Linear programming

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Dimension reduction (BS case)

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Asymptotic promotion

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Asymptotic promotion

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Asymptotic promotion

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Asymptotic promotion

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Asymptotic promotion