市大数学教室

大阪市立大学数学研究所
(Osaka City University Advanced Mathematical Institute)
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Friday Seminar on Knot Theory(2014年度)
2013年度
2014年度組織委員  岡崎 真也

講 演 者 :門田 直之 (大阪電気通信大学)
タ イ ト ル :Non-holomorphic Lefschetz fibrations with (-1)-sections
(アブストラクト) (PDF)
日 時 :4月25日(金)16:00~17:00
場 所 :数学 第3セミナー室(共通研究棟4階401室)
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講 演 者 :河村 建吾 (大阪市立大学)
タ イ ト ル :On the clasp number of a knot
(アブストラクト) (PDF)
日 時 :4月18日(金)16:00~17:00
場 所 :数学 第3セミナー室(共通研究棟4階401室)
Toptop
講 演 者 :植木 潤 (九州大学)
タ イ ト ル :On the universal deformations of SL(2)-representations of
2-bridge knot groups
(アブストラクト) (PDF)
日 時 :4月11日(金)16:00~17:00
場 所 :数学 第3セミナー室(共通研究棟4階401室)
Toptop



アブストラクト集



講 演 者: 門田 直之 (大阪電気通信大学)
タ イ ト ル: Non-holomorphic Lefschetz fibrations with (-1)-sections

The notion of Lefschetz fibrations in two-dimentional complex geometry (i.e., holomorphic Lefschetz fibrations) was generalized by Moishezon to four-dimensional topology. It is then natural to ask how far Lefschetz fibrations in four-dimensional topology are from holomorphic ones. To answer this question, various kinds of examples of non-holomorphic Lefschetz fibrations have been constructed. In particular, from Donaldson's theorem, it follows that there are infinitely many non-holomorphic Lefschetz fibrations with (-1)-sections. In this talk, we construct explicit examples of non-holomorphic Lefschetz fibrations with (-1)-sections without Donaldson's theorem. This is a joint work with Noriyuki Hamada (The university of Tokyo) and Ryoma Kobayashi (Tokyo university of science).

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講 演 者: 河村 建吾 (大阪市立大学)
タ イ ト ル: On the clasp number of a knot

Every knot in $S^{3}$ bounds a singular disk in $S^{3}$ whose singular set consists of only clasp singularities. The clasp number $c(K)$ of a knot $K$ is the minimal number of clasp singularities among all such singular disks bounded by $K$. In this talk, we determine the clasp number of a certain knot by using a characterization of the Alexander module, and we investigate the clasp numbers of $2$-bridge knots.
This is a joint work with T. Kadokami.

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講 演 者: 植木 潤 (九州大学)
タ イ ト ル: On the universal deformations of SL(2)-representations of
2-bridge knot groups

Joint work with M. Morishita, Y. Takakura and Y. Terashima.
In this talk, we first review Alexander-Fox theory and Iwasawa theory as the moduli theories of 1-dim. representations of knot/prime groups $G$. Then, we study the analogue story of prime groups, Hida-Mazur’s theory of 2-dim. representations, for knot groups:
(1) we overview the deformation theory of SL(2)-representation,
(2) state the relation between character variety and universal deformation ring, and
(3) construct the universal deformation of Riley's standard SL(2)-representation of 2-bridge knot group.
It should be remarked that In the dictionary of analogy in Arithmetic Topology, knots correspond to primes, and GL(2) Alexander polynomials $A(r,s)$ correspond to $p$-adic L-functions $L(r,s)$, where the parameters $s$ and $r$ come from GL(1) and SL(2) theories respectively.

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最終更新日: 2014年4月14日
(C)大阪市大数学教室