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Speaker:

Maggie Miller
Affiliation:

Stanford University/MPIM
Date:

Mon, 30/01/2023 - 15:00 - 16:00
Location:

MPIM Lecture Hall
Parent event:

MPIM Topology Seminar Hybrid.

Contact: T. Barthel, V. Ozornova, A. Ray, P. Teichner

With modern techniques, it is usually easy to determine when the complement of a knot in the 3-sphere admits a fibration over S^1. However, even though it is easy to prove the existence of such a fibration, I personally find it difficult to imagine this whole fibration (rather than just a single fiber). In this section of the talk, I’ll show how to explicitly produce fibrations on the complements of a natural family of knots so that we can see how every fiber intersects various cross-sections of S^3, and obtain a restrictive statement on the position of every fiber simultaneously. This will mostly involve a lot of 2-dimensional drawings and some very basic Morse theory.

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