Finite Quotients of Braid Groups Lily Li Joint Work with Alice - PowerPoint PPT Presentation

Aug 26, 2022 •512 likes •820 views

Finite Quotients of Braid Groups Lily Li Joint Work with Alice Chudnovsky, Caleb Partin, and Kevin Kordek Consider... Given two groups G, H, what are all the homomorphisms between them? Braid Group Braid Group Main Result Finite Quotients

Finite Quotients of Braid Groups Lily Li Joint Work with Alice Chudnovsky, Caleb Partin, and Kevin Kordek
Consider... Given two groups G, H, what are all the homomorphisms between them?
Braid Group
Braid Group
Main Result Finite Quotients of Braid Groups
Fundamental Lemma of Totally Symmetric Sets The image of a totally symmetric set under a homomorphism is a totally symmetric set.
Fundamental Lemma of Totally Symmetric Sets The image of a totally symmetric set under a homomorphism is a totally symmetric set. BUT IT GETS BETTER
Fundamental Lemma of Totally Symmetric Sets The image of a totally symmetric set of size n under a homomorphism is a totally symmetric set of size n or 1.
Our favorite totally symmetric set
Our favorite totally Image of S: also totally symmetric set symmetric set
Our favorite totally Image of S: also totally symmetric set symmetric set
The image of S is either... singleton Then the map is cyclic
The image of S is either... a singleton not a singleton Then the map is The stabilizer of S in G Its image is large: contains a cyclic copy of S n
Case 2: Not singleton
Case 2: Not singleton
Case 2: Not singleton Stabilizer of the totally symmetric set
Case 2: Not singleton Size of the totally symmetric set Stabilizer of the totally symmetric set
Case 2: Not singleton Elements inducing trivial permutation All the elements that permute S
Case 2: Not singleton
Bounds on Sizes of Totally Symmetric Sets

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