stable commutator length in graphs of groupsmath.uchicago.edu/~lzchen/slides/sclbs_talk.pdf · in...
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![Page 1: 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](https://reader036.vdocuments.us/reader036/viewer/2022081614/5fc59b76c932c1371b7a8e3d/html5/thumbnails/1.jpg)
Lvzhou Chen
Stable commutator length
in graphs of groups
NCNGT 1
Lvzhou Chen
NCNGT
May 27, 2020
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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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Lvzhou Chen NCNGT 4
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