finite quotients of braid groups
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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


  1. Finite Quotients of Braid Groups Lily Li Joint Work with Alice Chudnovsky, Caleb Partin, and Kevin Kordek

  2. Consider... Given two groups G, H, what are all the homomorphisms between them?

  3. Braid Group

  4. Braid Group

  5. Main Result Finite Quotients of Braid Groups

  6. Fundamental Lemma of Totally Symmetric Sets The image of a totally symmetric set under a homomorphism is a totally symmetric set.

  7. 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

  8. 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.

  9. Our favorite totally symmetric set

  10. Our favorite totally Image of S: also totally symmetric set symmetric set

  11. Our favorite totally Image of S: also totally symmetric set symmetric set

  12. The image of S is either... singleton Then the map is cyclic

  13. 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

  14. Case 2: Not singleton

  15. Case 2: Not singleton

  16. Case 2: Not singleton Stabilizer of the totally symmetric set

  17. Case 2: Not singleton Size of the totally symmetric set Stabilizer of the totally symmetric set

  18. Case 2: Not singleton Elements inducing trivial permutation All the elements that permute S

  19. Case 2: Not singleton

  20. Bounds on Sizes of Totally Symmetric Sets

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