Mdtop April 2021

mdtop@mathdept.okstate.edu

1 participants
2 discussions

Topology seminar tomorrow 4/21
by Hoffman, Neil 20 Apr '21

20 Apr '21

Hello everyone, Tomorrow I am speaking in seminar. I am actually speaking about a question Robert asked about in seminar back when we are in person. My title and abstract are below: Title: Recovering knot diagrams from triangulations Speaker: Neil Hoffman, Oklahoma State University Date: Apr 21, 2021 Time: 3:30 PM Room: https://meet.google.com/frv-bgow-byi Abstract: While the study of knots originally was related to manipulating knot diagrams, one often studies knots by analyzing their complements. In fact, Gordon and Luecke showed two knots are equivalent if and only if their complements are homeomorphic. There are wellknown procedures for constructing a knot complement from a knot diagram. We will analyze the problem from the other perspective: constructing a knot diagram from a triangulated knot complement and describe an algorithm to produce such a diagram. This is joint work Robert Haraway, Saul Schleimer and Eric Sedgwick. ______________________ 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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Today (Wednesday) in Topology Seminar
by Hoffman, Neil 07 Apr '21

07 Apr '21

We are very happy to have Alex Zupan joining us from University of Nebraska. His title and abstract are below. Title: Complex curves in CP^2 from the perspective of bridge trisections Speaker: Alex Zupan, University of Nebraska Date: Apr 7, 2021 Time: 3:30 PM Room: https://meet.google.com/frv-bgow-byi Abstract: Peter Lambert-Cole and Jeff Meier revealed that bridge trisections of complex curves in CP^2 exhibit elegant structure: Every complex curve admits an inefficient shadow diagram (with respect to the standard genus one trisection) in which shadow arcs form a hexagonal lattice in the torus. Additionally, Lambert-Cole proved a combinatorial classification of symplectic surfaces in CP^2 : A surface that minimizes genus in its homology class is symplectic if and only if it admits a transverse shadow diagram. We prove a complex version of Lambert-Cole’s theorem, that a genus-minimizing surface in CP^2 is complex if and only if it admits a transverse hexagonal lattice diagram. In the process, we find infinite families of efficient hexagonal lattice diagrams for complex curves, and we give a combinatorial characterization of the symplectic isotopy problem in CP^2 ______________________ 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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Mdtop April 2021