Hello everyone,

Today we have an OSU alum Bo-hyun Kwon speaking in seminar today. He is visiting from Korea University. He will be visiting for the next two weeks and using the spare office on the fifth floor.

His title and abstract are below:

Title: The Rectangle condition and its applications

Speaker: Bo-hyun Kwon, Korea University

Date: Feb 12, 2019

Time: 3:30 PM

Room: MSCS 509

Abstract: In this talk, we define the rectangle condition and connecting rectangle condition to check whether or not a Heegaard splitting is strongly irreducible which is a variation of the rectangle condition by Casson and Gordon. Moreover, with a similar condition defined on a n-bridge decomposition, we can check whether or not the Hempel distance of a n-bridge decomposition is greater than or equal to two. Then, we can define a generalized rectangle condition. We also give specific examples for Heegaard splitting of 3-manifolds and n-bridge decomposition of knots which satisfy the connecting rectangle condition.

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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