2005年10月 -- 2006年1月
[English]
[過去のプログラム]
16:30 -- 18:00 数理科学研究科棟(東京大学駒場キャンパス)
Tea: 16:00 -- 16:30 コモンルーム
Last updated January 18, 2006
世話係
河野俊丈
河澄響矢
10月11日 -- 056号室, 16:30 -- 18:00
Vincent Blanloeil (IRMA, Univ. Louis Pasteur)
Cobordism of surfaces embedded in S4
Abstract:
In this talk I will introduce cobordism of knots, and recall classical results
of this theory. Then I will explain the results of a join work with O. Saeki,
in which we gave a classification of embedded surfaces in S4 up to cobordism.
As a consequence I will give a new proof of Rohlin's theorem on
3-manifolds embeddings in R5.
10月18日 -- 056号室, 16:30 -- 18:00
Andrei Pajitnov (Univ. de Nantes)
Novikov homology, twisted Alexander polynomials,
and Thurston norm
Abstract:
We discuss circle-valued Morse functions on
complements to links in the 3-sphere.
A generalization of Morse theory due to S.P.Novikov
leads to computable numerical estimates of the number
of critical points via the twisted Novikov homology,
introduced in a paper of H.Goda and the author. We
discuss a multi-variable analog of the twisted Novikov
homology and its relations to the multi-variable
twisted Alexander polynomials and the Thurston norm.
10月25日 -- 056号室, 16:30 -- 18:00
Daniel Matei (Institute of Mathematics of the Romanian Academy)
The local system homology of pure braids on
surfaces
Abstract: Pure braid groups of surfaces, either
closed or punctured, admit the structure of an
iterated extension by free groups. This structure
allows us to construct resolutions of the pure braid
groups over the integers. These resolutions are then
used to derive information on the rank one local
system homology of the pure braids on surfaces.
11月1日 -- 056号室, 16:30 -- 18:00
吉永 正彦 (京都大学数理解析研究所)
実超平面配置と Lefschetz の超平面切断定理
Lefschetz の超平面切断定理は複素代数多様体のトポロジーに関する
最も基本的な結果で、代数多様体のセル分割に必要なセルの
次元、枚数などに関する応用があります。しかし一方、セルの貼付き方については
一般的には何も分かりません。実数体上定義された超平面配置の
補集合に Lefschetz の定理を適用した際のセルの貼付き方を、実領域の
組合せ論的構造を使って記述する、という結果の紹介をします。
11月14日〜11月18日 集中講義 遠藤 久顕 （大阪大学理学研究科）
11月22日 -- 056号室, 16:30 -- 18:00
坪井 俊 (東京大学大学院数理科学研究科)
実解析的微分同相群の完全性について
実解析的多様体の実解析的微分同相の群は，
$C^\infty$級微分同相群の中で稠密な巨大な群である．
Hermanが$n$次元トーラスの実解析的微分同相群の恒等写像の連結成分は
単純群であることを示している．
本講演では，もう少し広い範囲の多様体，多重有向円周束構造を持つ多様体および球面の
積に対して，恒等写像の連結成分の群は
完全群であることを示す．
11月29日 -- 056号室, 16:30 -- 18:00
塚本 達也 (早稲田大学理工学部)
The almost alternating diagrams of the trivial knot
Abstract: Bankwitz characterized an alternating diagram representing the trivial knot.
A non-alternating diagram is called almost alternating if
one crossing change makes the diagram alternating.
We characterize an almost alternaing diagram representing the trivial knot.
As a corollary we determine an unknotting number one alternating knot with
a property that the unknotting operation can be done on its alternating diagram.
12月6日 -- 056号室, 17:00 -- 18:00
山口 孝男 氏 (筑波大数学)
曲率が上に有界な2次元アレクサンドロフ空間の局所構造
曲率が上に有界な距離空間(アレクサンドロフ空間)の局所構造は、曲率が下に有界な場合と異なり複雑でよく分かっていない。ここでは空間が2次元である場合の局所構造についての結果をお話しする。
12月13日 -- 056号室, 16:30-- 18:00
Andres Navas (Universidad de Chile)
On the best regularity for group actions on the interval
Given a continuous action of a finitely generated group on the interval,
we will investigate what is the best regularity that can be achieved
by performing topological conjugacies. As we will see, all the
problem concentrates between the classes C1 and C2.
12月20日 -- 056号室, 16:30-- 18:30
桑子 和幸 (東京大学大学院数理科学研究科)
Dehn surgery creating Klein bottles
We consider the situation that Dehn surgery on a knot in the $3$-sphere
yields Klein bottles.
Fix a knot $K \subset S^{3}$ and let $M$ be a complement.
Assume that Dehn surgered manifolds
$M(r)$ and $M(s)$ both contain Klein bottles.
We discuss the geometric intersection number between such two slopes
$r$ and $s$.
長谷川 功 (東京大学大学院数理科学研究科)
Chart description of monodromy representations
on a closed surface.
Abstract:
In surface-knot theory, S. Kamada introduced chart description
to visualize a monodromy representation of a $2$-dimensional braid.
We define a chart description for a monodromy representation
on a closed surface valued in $G$.
As an application, we describe chart move equivalences
for Lefschetz fibrations and $(Z_2)^m\rtimes S_m$-monodromies.
1月10日 -- 056号室, 16:30-- 18:30
田所 勇樹 (東京大学大学院数理科学研究科)
A nontrivial algebraic cycle in the Jacobian variety of the Klein
quartic
Abstract:
B. Harris defined the harmonic volume for a compact Riemann surface of
genus $g\geq 3$, by means of Chen's iterated integrals.
We prove some value of the harmonic volume for the Klein quartic $C$ is
nonzero modulo $\frac{1}{2}\mathbb{Z}$, using special values of the
generalized hypergeometric function.
This result tells us the algebraic cycle $C-C^-$ is not algebraically
equivalent to zero in the Jacobian variety $J(C)$.
八嶋 洋行 (東京大学大学院数理科学研究科)
The primitive vector field and semi-analytic geometry
of reflection groups
Abstract:
The aim of this seminor is to investigate relations
between geometry of a finite irreducible reflection group
and that of its parabolic subgroups.
Fundamental tools are the discriminant of reflection hyperplanes and
the primitive vector field in the categorical quotient space of
reflection group actions. Both of them play important roles in
the theory of the flat (Frobenius) structure of reflection groups and
construction of a semi-algebraic dual polyhedron, invented by K. Saito.
I show that a connected component of common zero point set of
algebroid functions defined by the discriminant
is equivariant homeomorphic to a real vector space
whose dimension is equal to the rank of a parabolic subgroup.
In particular the case that a parabolic subgroup is of corank 1,
this homeomorphism can be extended to semi-analytic diffeomorphism.
1月17日 -- 056号室, 16:30 -- 18:00
Ryan Budney (Max Planck Institute)
Topology of spaces of knots
Abstract: I will describe what is known about the homotopy-type of the
space of smooth embeddings of a j-sphere in an n-sphere, Emb(S^j,S^n), and
a closely related space K_{n,j}, the space of "long embeddings" of R^j in
R^n. I will try to survey the "group like" properties of these spaces:
Haefliger's work on the isotopy classes of embeddings of S^j in S^n as
monoids under the connected sum operation, and the iterated loop-space
structures on certain "framed" analogues of K_{n,j}. There are results
of Goodwillie and Weiss on the connectivity of K_{n,j} and Emb(S^j,S^n),
and some computations of non-trivial homotopy groups of K_{n,1} for n>3
due to Sinha, Scannell, Longoni and Cattaneo. I will also give a
description of the homotopy type of Emb(S^1,S^3) and K_{3,1}. The
homotopy type of K_{3,1} is given recursively. Each component of K_{3,1}
is described as the total space of a fiber bundle where the fiber is a
product of "simpler" components of K_{3,1} and the base space can be one
of various "elementary" spaces such as configuration spaces in R^2, and
products of circles.
1月24日 -- 056号室, 16:30-- 18:30
佐伯 真一 (東京大学大学院数理科学研究科)
Incompressible surfaces in 4-punctured sphere bundles
Abstract:
Hatcher and Thurston classified the incompressible
surfaces in the 2-bridge knot complements.
And Floyd and Hatcher classified the incompressible
surfaces in the 2-bridge link complements
and in the punctured torus bundles over the circle.
A natural extension of the technique used in these works
is to apply for the classification of the incompressible surfaces
in the 4-punctured sphere bundles over the circle.
Indeed,
Floyd and Hatcher mentioned this as a Remark in their paper.
These works do not consider the connectedness of the surfaces.
In this seminar,
we will give a criterion for
the connectedness and (non-)orientability
of an incompressible surface
of 2-bridge knot complement type
in 4-punctured sphere bundles over the circle,
and give the list
of such surfaces with genus 0 or 1.
横山 知郎 (東京大学大学院数理科学研究科)
各葉の基本群が同型な余次元一極小葉層構造
内容は、以下の二つを示すことです。
1.$F$を、横断的に実解析的、かつ横断的に向き付け可能な余次元1の極小葉層構
造とする
。このとき、$F$の各葉の基本群が$Z$と同型ならば、$F$はホロノミーを持たな
い。
2.Mを二次のホモトピー群が自明であるような多様体とする。
$F$を、M上の横断的に実解析的、かつ横断的に向き付け可能な余次元1極小葉層
構造とす
る。このとき、$F$の各葉が$Z^k$と同型ならば、$F$はホロノミーを持たない。