Mdtop September 2020

mdtop@mathdept.okstate.edu

2 participants
3 discussions

Tomorrow in topology seminar
by Hoffman, Neil 15 Sep '20

15 Sep '20

Tomorrow we have Josh Howie "coming" to speak at 3:45 central. The meeting link will be https://meet.google.com/frv-bgow-byi His title and abstract are below: Alternating genera of torus knots Speaker: Josh Howie, UC Davis Date: Sep 16, 2020 Time: 3:45 PM Room: https://meet.google.com/frv-bgow-byi Abstract: The alternating genus of a knot is the minimum genus of a surface onto which the knot has an alternating diagram satisfying certain conditions. Very little is currently known about this knot invariant. We study spanning surfaces for knots and define an alternating distance from the extremal spanning surfaces. This gives a lower bound on the alternating genus and can be calculated exactly for torus knots. We prove that the alternating genus can be arbitrarily large, find the first examples of knots where the alternating genus is exactly 3, and classify all toroidally alternating torus knots. ______________________ Neil R. Hoffman Assistant Professor Department of Mathematics 523 Math Science Building Oklahoma State University Stillwater, OK 74078-1058 405-744-7791 http://math.okstate.edu/people/nhoffman

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Topology seminar at 3:45 today!
by Hoffman, Neil 09 Sep '20

09 Sep '20

Hello everyone, Today's seminar will use the same link as last week: meet.google.com/bqo-wbtp-gzj Thomas Kindred from University of Nebraska will be joining us. His title and abstract are below: A geometric proof of the flyping theorem Speaker: Thomas Kindred, University of Nebraska Date: Sep 9, 2020 Time: 3:45 PM Room: Virtual meeting Abstract: In 1898, Tait asserted several properties of alternating knot diagrams. These assertions came to be known as Tait’s conjectures and remained open through the discovery of the Jones polynomial in 1985. The new polynomial invariants soon led to proofs of all of Tait’s conjectures, culminating in 1993 with Menasco-Thistlethwaite’s proof of Tait’s flyping conjecture. In 2017, Greene gave the first geometric proof of part of Tait’s conjectures, while also answering a longstanding question of Fox by characterizing alternating links geometrically; Howie independently answered Fox’s question with a related characterization. I will use these new characterizations, among other techniques, to give the first entirely geometric proof of Menasco-Thistlethwaite’s Flyping Theorem. ______________________ Neil R. Hoffman Assistant Professor Department of Mathematics 523 Math Science Building Oklahoma State University Stillwater, OK 74078-1058 405-744-7791 http://math.okstate.edu/people/nhoffman

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Topology Seminar, 3:45-4:45, Wednesday Sept 2
by Henry Segerman 01 Sep '20

01 Sep '20

Hi all, I will be speaking this week. ***Note the new Google Meet link:*** meet.google.com/bqo-wbtp-gzj Title: From veering triangulations to Cannon-Thurston maps Abstract: Agol introduced veering triangulations of mapping tori, whose combinatorics are canonically associated to the pseudo-Anosov monodromy. In previous work, Hodgson, Rubinstein, Tillmann and I found examples of veering triangulations that are not layered and therefore do not come from Agol’s construction. However, non-layered veering triangulations retain many of the good properties enjoyed by mapping tori. For example, Schleimer and I constructed a canonical circular ordering of the cusps of the universal cover of a veering triangulation. Its order completion gives the veering circle; collapsing a pair of canonically defined laminations gives a surjection onto the veering sphere. In work in progress, Manning, Schleimer, and I prove that the veering sphere is the Bowditch boundary of the manifold’s fundamental group. As an application we produce Cannon-Thurston maps for all veering triangulations. This gives the first examples of Cannon-Thurston maps that do not come, even virtually, from surface subgroups.

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Mdtop September 2020