[geometry-ml:06821] 金沢トポロジーセミナー（5/28 植木 潤 氏（お茶の水女子大学）, 6/4 昆 万佑子 氏（信州大学））

[kadokami ＠ se.kanazawa-u.ac.jp]

各位

金沢大学の門上、滝岡、丸山、宮地です。

いつもお世話になっております。


金沢大学にてトポロジーセミナーを開催いたしますのでご連絡いたします。

https://sites.google.com/view/kanazawatopseminar/


複数のメーリングリストにご案内しております。重複をどうかお許しください。

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2026年5月28日（木）

• 時間：15：00〜16：00

• 講演者： 植木 潤（お茶の水女子大学）

• Zoomによるオンライン講演と対面講演の併用

• タイトル : Profinite rigidity of the taut polynomials of
fibered hyperbolic 3-manifold groups

アブストラクト :
It is a highly interesting question to ask which property of a
3-manifold is profinitely rigid, namely, which geometric, dynamical,
or topological property of a 3-manifold the isomorphism class of the
profinite completion determines.
In this talk, we establish profinite rigidities of the twisted
multivariable Alexander polynomials of hyperbolic manifolds under
regularity conditions, a pseudo-Anosov map on a surface being fully
punctured, the Teichmüller/taut polynomials of fibered faces of the
Thurston norm balls of hyperbolic 3-manifolds (fully punctured cases
and filled-cases), and three specific hyperbolic one-cusped
3-manifolds determined by a strategy using normalized dilatations
and the veering census.
The taut polynomial is an invariant introduced by
Landry--Minsky--Taylor, generalizing McMullen's Teichmuller
polynomials. Parlak proved that it may be regarded as a twisted
Alexander polynomial.
Combining Tsang's result on small dilatation and using the veering
census, we obtain concrete new examples.
A key idea is the celebrated correspondence amongst fibered faces of
the Thurston norm ball, suspension pseudo-Anosov flows, and layered
veering triangulations on the exterior of the singular fibers of a
hyperbolic 3-manifold pioneered by Thurston, Fried, Agol, and
others.
We also utilize the profinite rigidities of the Thurston norm balls
and Dehn fillings, as well as regularity theorems founded by Liu and
Xu.
We remark that
・The analogy between Alexander--Fox theory and Iwasawa theory in
arithmetic topology helps.
・The closed orbits of a pseudo-Anosov flow on a closed 3-manifold
behave like prime numbers, namely, obey the Chebotarev law.
This talk is based on a joint work with Tam Cheetham-West (Yale U.),
Biao Ma (Tongji U), and Youheng Yao (Yale U.).

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2026年6月4日（木）

• 時間：15：00〜16：00

• 講演者： 昆 万佑子（信州大学）

• Zoomによるオンライン講演

• タイトル : An orientation-free reconstruction of B-type
coefficient polynomials via Kawauchi's approach

アブストラクト :
Kawauchi introduced coefficient polynomials, showing that, when the
HOMFLY polynomial (an A-type link polynomial) is regarded as a
formal power series, each coefficient itself becomes a link
invariant equipped with a skein-theoretic structure. The existence
proof is based on a double induction on the crossing number and the
warping degree.

In this talk, we show that a similar approach can be extended to the
Kauffman polynomial, one of the fundamental B-type link polynomials.
However, the original double induction does not work directly in the
B-type setting. To overcome this difficulty, we enlarge the initial
stage of the induction to connected sums of monotone diagrams.
Moreover, since the four-term skein relation generally involves
smoothings that do not preserve orientation, the grading of the
coefficient polynomials must also be defined in an orientation-free
manner.

With these modifications, we prove that Kawauchi's approach extends
to the Kauffman polynomial. If time permits, we will also discuss
the uniqueness of the resulting coefficient polynomials.

(This is joint work with Noboru Ito. arXiv: 2603.25402)

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※ Zoomでの参加を希望される方は、講演日の前日までに登録フォーム

https://docs.google.com/forms/d/e/1FAIpQLSdeJBfBkzUmaS49Zaxm5Wi2Mrj6kdaWpRI1gyAbaw0ivMelrw/viewform

にお名前、所属等の情報をご記入下さい。講演時間までにZoomアドレスをお伝えします。なお、このZoomアドレスは今年度のセミナーでは共通となります。すでにお送りした方々は今回ご連絡の必要はありません。

※ 
対面の場所は自然科学5号館数学・管理棟4階471号室（コロキウム3）です。対面での参加を希望される方は、講演日の前日までに宮地（miyachi ＠ se.kanazawa-u.ac.jp）までお名前、所属等の情報をお知らせ下さい。

皆様のご参加をお待ちしております。
よろしくお願いいたします。


金沢トポロジーセミナーでは講演者を募集しております。

ご興味のおありの方は世話役までお気軽にご連絡ください。

門上晃久（kadokami ＠ se.kanazawa-u.ac.jp）
滝岡英雄（takioka ＠ se.kanazawa-u.ac.jp）
丸山修平（smaruyama ＠ se.kanazawa-u.ac.jp）
宮地秀樹（miyachi ＠ se.kanazawa-u.ac.jp）
（金沢大学）