Loops in surfaces, chord diagrams and their interlace graphs : minimal genus

Meeting Details

For more information about this meeting, contact Rachel Weaver, Ping Xu, Mathieu Stiénon.

Speaker: Christopher-Lloyd Simon, Penn State

Abstract: Consider a generic loop in a surface, and label its intersections to obtain a cyclic word with each letter appearing twice, that is a chord diagram. Gauss wondered which chord diagrams arise from loops in the sphere and found two necessary conditions, which he knew were not sufficient. This Gauss-realizability problem has attracted much interest and after many decades of research several characterisations have been (dis)proved. We will recover the description proposed by Rosenstiehl, which only depends on the the interlace graph of the chord diagram, and generalise it to loops surfaces of higher genus. Chord diagrams and their interlace graphs are powerful invariants in various (knot) theories, and many questions about them remain open. We will only assume some acquaintance with the language of cohomology, and (give you) a taste for combinatorial topology.

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Room Reservation Information

Room Number: 106 McAllister

Date: 02/20/2024

Time: 2:30pm - 3:30pm