Intrinsic Chirality of Graphs in 3-manifolds

Date: 
Friday, 29 July, 2016 - 16:00 - 17:00
Venue: 
LSB 222
Seminar Type: 
Seminar
Speaker Name: 
Prof. Erica FLAPAN
Affiliation: 
Pomona College
Abstract: 

We say that an embedding Γ of a graph γ in a 3-manifold M is achiral if there is an orientation reversing homeomorphism of (M, Γ). If a graph γ has no such embedding in M we say γ is intrinsically chiral in M.

We prove that for any closed, connected, orientable, irreducible 3-manifold M, there is an integer nM such that every 3-connected graph γ with genus (γ) > nM and no involution is intrinsically chiral in M. On the other hand, we prove that every graph has achiral embeddings in infinitely many closed, connected, orientable, irreducible 3-manifolds.