## Friday Seminar on Knot Theory（2018年度）

 日時 2018年6月8日（金）16：00～17：00 講演者（所属） 和田 康載（早稲田大学） タイトル Generalized virtualization on welded links 場所 理学部 Ｆ棟 415号室（中講究室） アブストラクト For each positive integer $n$ we introduce two local moves $V(n)$ and $V^n$, which are generalizations of the virtualization move. We give a classification of welded links up to $V(n)$-move. In particular, a $V(n)$-move is an unknotting operation on welded knots for any $n$. On the other hand, we give a necessary condition for which two welded links are equivalent up to $V^{n}$-move. This leads to show that a $V^{n}$-move is not an unknotting operation on welded knots except $n=1$. We also discuss relations among $V^{n}$-moves, associated core groups and the multiplexing of crossings. This is a joint work with Haruko A. Miyazawa and Akira Yasuhara.
 日時 2018年5月25日（金）16：00～17：00 講演者（所属） 村尾　智（筑波大学） タイトル Necessary conditions to be constituent handlebody-knots and their application 場所 理学部 Ｆ棟 415号室（中講究室） アブストラクト For a handlebody-knot $H$, a constituent handlebody-knot of $H$ is a handlebody-knot obtained from $H$ by removing an open regular neighborhood of some meridian disks of $H$. We can deal with the tunnel number and the cutting number uniformly, which are “dual” geometric invariant for handlebody-knots, by introducing the notion of constituent handlebody-knots. In this talk, we provide necessary conditions to be constituent handlebody-knots by using $G$-family of quandles colorings. Furthermore we give lower bounds for the tunnel number and the cutting number of handlebody-knots as the corollaries.
 日時 2018年5月18日（金）16：00～17：00 講演者（所属） 久野 恵理香 (大阪大学) タイトル Abelian subgroups of the mapping class groups for non-orientable surfaces 場所 理学部 Ｆ棟 415号室（中講究室） アブストラクト One of the basic and important problems to study algebraic structures of mapping class groups is finding abelian subgroups included in the mapping class groups. Birman-Lubotzky-McCarthy in 1983 gave an answer to this question for the orientable surfaces. In this talk, we give the upper bound of the torsion-free rank of the abelian subgroups for the mapping class groups of non-orientable surfaces.
 日時 2018年5月11日（金）16：00～17：00 講演者（所属） 金信 泰造 (大阪市立大学) タイトル Classification of ribbon 2-knots by the twisted Alexander polynomials 場所 理学部 Ｆ棟 415号室（中講究室） アブストラクト We have classified the oriented ribbon 2-knots presented by virtual arcs with up to four crossings. In this talk, we consider this classification using the twisted Alexander polynomial associated to SL(2,C)-representation. We also announce some properties of the twisted Alexander polynomial of a ribbon 2-knot with one fusion.
 日時 2018年4月27日（金）16：00～17：00 講演者（所属） Jung Hoon Lee（Chonbuk National University） タイトル On weak reducing disks and disk surgery 場所 理学部 Ｆ棟 415号室（中講究室） アブストラクト Let $K$ be an unknot in $8$-bridge position in the $3$-sphere. We give an example of a pair of weak reducing disks $D_1$ and $D_2$ for $K$ such that both disks obtained from $D_i$ ($i = 1, 2$) by a surgery along any outermost disk in $D_{3-i}$, cut off by an outermost arc of $D_i \cap D_{3-i}$ in $D_{3-i}$, are not weak reducing disks, i.e. the property of weak reducibility of compressing disks is not preserved by a disk surgery.
 日時 2018年4月20日（金）16：00～17：00 講演者（所属） 阿部 翠空星 (OCAMI) タイトル Perturbative $\mathfrak{g}$ invariants of genus $2$ handlebody-knots 場所 理学部 Ｆ棟 415号室（中講究室） アブストラクト We denote perturbative $\mathfrak{sl}_2$ invariants of genus $2$ handolebody-knots. We try to define a perturbative $\mathfrak{g}$ invariant for the general Lie algebra. This definition is not yet definitely completed definitions. I want the opinions of many people of mathematician.
 日時 2018年4月13日（金）16：00～17：00 講演者（所属） 岡﨑 建太（京都大学数理解析研究所） タイトル On planar algebras and state sum invariants of 3-manifolds 場所 理学部 Ｆ棟 415号室（中講究室） アブストラクト Theory of subfactors has many applications in low dimensional topology, including Jones polynomial of knots, quantum invariants and state sum invariants of $3$-manifolds. Planar algebras, on the other hand, which are defined by using planar operad, enable us to treat extremal subfactors combinatorially. In this talk, we briefly introduce the basic concept of planar algebras, and explain how to construct state sum invariants of $3$-manifolds. In particular, we give an explicit construction of the state sum invariant of $3$-manifolds derived from the subfactor with principal graph $E_8$.