Knotting Nagoya 2021

結び目の数理セミナー Knotting Nagoya 会合案内



日時(Date):2021 Aug 7th(Sat)09:30 ~ 11:30 (Japan time)

場所(Place) : on ZOOM (URL to be inquired)

予定(Schedule): Presentation for about an hour and following up discussion

講演者(speaker): 寺垣内 政一(Masakazu Teragaito, Hiroshima University)

タイトル(Title): Identifying non-pseudo-alternating knots by using the free factor property of minimal genus Seifert surfaces

アブストラクト(Abstract): MaylandとMurasugiが1976年に導入した pseudo-alternating knotという概念がある.それは, alternating knotを含む広いクラスである. primitive flat surfaceとよばれるSeifert surfaceを村杉和して得られる曲面の 境界として定義される. したがって,pseudo-alternating knotを構成することは容易だが, 与えられた結び目がpseudo-alternatingかどうかを判定することは 一般には困難である. この講演では,最小種数Seifert surfaceのもつfree factor propertyという 性質に着目して,ある種のpretzel knotがpseudo-alternatingでないことを 示す.これにより,特に,rationally homologically fibered knotではあるが pseudo-alternatingではない結び目の存在を,任意の種数に対して確認できる. 議論の一端をになう最小種数Seifert surfaceの一意性については, 小林毅氏によるsutured manifold theoryを用いた議論を援用する. (姫野圭佑氏(広島大学大学院先進理工系科学研究科)との共同研究)

Abstract: Pseudo-alternating knots and links are defined constructively via their Seifert surfaces. By performing Murasugi sums of primitive flat surfaces, such a knot or link is obtained as the boundary of the resulting surface. Conversely, it is hard to determine whether a given knot or link is pseudo-alternating or not. A major difficulty is the lack of criteria to recognize whether a given Seifert surface is decomposable as a Murasugi sum. In this talk, we propose a new idea to identify non-pseudo-alternating knots. Combining with the uniqueness of minimal genus Seifert surface obtained through sutured manifold theory, we demonstrate that two infinite classes of pretzel knots are not pseudo-alternating. (This is a joint work with Keisuke Himeno.)


「Knotting Nagoya and N.Y. 」
Date:2021 Apr 17th(Sat)10:00 ~ 11:00 (Japan time)
Place : on ZOOM (URL to be inquired)

10:00-10:05 Opening and introduction of the speaker
10:05-10:50 Talk by P. Ording
10:50-11:00 Q&A and discussion
After closing, open chat time for a while.

Speaker: Philip Ording (Sarah Lawrence College)
Title: A random walk through proof space

Abstract. Paul Erdős imagined that in heaven God has a book--"The Book"--and in it is written the best proof of any theorem. Putting theology aside there is some disagreement about whether the set of proofs admits such an ordering. For example John Conway and Joseph Shipman argued that we "shouldn’t speak of 'the best' proof, because different people will value proofs in different ways. Indeed one person’s value might oppose another’s." Instead they envisioned a multidimensional space of proofs. This informal talk will explore the proof space populated by the book 99 Variations on a Proof which appeared in a Japanese edition, 1つの定理を証明する99の方法, earlier this year.












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Knotting Nagoyaは名古屋工業大学, 名古屋市立大学, 名城大学, 愛知教育大学, 名古屋大学の専門家にて共同運営しております.


OCAMI:大阪市立大学 数学研究所