講演・口頭発表等

招待有り 本文へのリンクあり 国際会議
2020年8月28日

Unknotting operations, crosscap numbers, and volume bounds (full proofs)

Quantum Topology Seminar (MSCS, Chicago)
  • Noboru Ito

記述言語
英語
会議種別
口頭発表(招待・特別)
主催者
L. H. Kauffman
開催地
Chicago
国・地域
アメリカ合衆国

In this talk, we introduce two invariants to compute the crosscap number for any alternating knot.  One of the two invariants is given by band surgery and the other one is of splicing.   For the former, it is easy to see the correspondence between band surgeries and crosscap numbers.  For the latter, though the proof is more technical than the former, we have a general argument of computations for crosscap numbers including those of alternating knots and some non-alternating knots.   Further, we discuss a relationship between our invariants and known bounds with respect to the Jone polynomial or hyperbolic volume bounds.
This is a joint work with Yusuke Takimura (Gakushuin Boys’ Junior High School)

Paper's PDF: https://www.worldscientific.com/doi/epdf/10.1142/S0129167X20501116

リンク情報
共同研究・競争的資金等の研究課題
バシリエフ不変量の圏論化の探究と展開
URL
http://homepages.math.uic.edu/~kauffman/ 本文へのリンクあり
URL
https://www.dropbox.com/sh/5c3xihm2mkdo5s5/AADl_aRwAB3EfT2YpiLfCRZ-a?dl=0 本文へのリンクあり