16:30 -- 18:00 Ȋwȓ()
Tea: 16:00 -- 16:30 R[

107 -- 056, 16:30 -- 18:00

Remi Langevin (Univ. de Bourgogne)

The space of spheres and some application to curves and surfaces

After explaining how the space of spheres can be identified with de Sitter quadric $$x_1^2+...+x_4^2 -x_5^2 =3D 1 \subset {\bf L^5}$$ given a modern presentation of Darboux' pentaspheric coordinates, we will construct the conformal Gauss image of Bryant, and comment Willmore Conjecture.

Then we will define a conformal invariant of curves or links: the conformal modulus, and show its relations with the space of spheres. A few results and many questions on knots and links will follow.

1014 -- 122, 16:30 -- 18:00

{c (Southern California w)

Cabling and transverse simplicity

X^_[hȐڐGOʂ Legendre іڂ transverse іڂ̕ނ̌ʂЉB(John Etnyre Ƃ̋B)

1028 -- 056, 16:30 -- 18:00

Elmar Vogt (BerlinRw)

Tangential Lusternik-Shnirelman Category for Foliations

Abstract: By definition the Lusternik-Shnirelman category of a space X is one less than the smallest number ofcategorical open sets needed to cover X. A set in X is called categorical if it is contractible in X. This concept was generalized by Hellen Colman to foliated manifolds where an open set U is categorical if the inclusion of U can be homotoped by a leafwise (i.e. tangential) homotopy to a map which sends every leaf of the foliation induced on U to a point.

In the talk we will discuss this definition explain its role with regard to the dynamics of the foliation, and present results about upper and lower bounds for this new numerical invariant for foliations.

114 -- 056, 16:30 -- 18:00

Christophe EYRAL (Tokyo Metropolitan Univ. / JSPS)

1-equivalent Zariski pairs

Consider a moduli space ${\cal M}(\Sigma,d)$ of reduced curves in $\hbox{\a CP}^2$ with a given degree~$d$ and having a prescribed configuration of singularities $\Sigma$. Let $C, C'\in {\cal M}(\Sigma,d)$. The pair of curves $(C,C')$ is called a Zariski pair if the pairs of spaces $(\hbox{\a CP}^2,C)$ and $(\hbox{\a CP}^2,C')$ are not homeomorphic. There exists two classical ways to detect Zariski pairs: (i) showing that the generic Alexander polynomials $\Delta_C(t)$ and $\Delta_{C'}(t)$ of $C$ and $C'$, respectively, are different; (ii) showing that the fundamental groups $\pi_1(\hbox{\a CP}^2-C)$ and $\pi_1(\hbox{\a CP}^2-C')$ are not isomorphic. In this talk, we shall give the first example of a Zariski pair $(C,C')$ such that $\pi_1(\hbox{\a CP}^2-C)$ and $\pi_1(\hbox{\a CP}^2-C')$ are isomorphic (notice that such an isomorphism automatically implies $\Delta_C(t) = \Delta_{C'}(t)$). We shall call such a Zariski pair a $\pi_1$-equivalent Zariski pair. The members $C$ and $C'$ of our pair are reducible sextics with the following configuration of singularities $\{D_{10}+A_5+A_4\}$. By the way, we determine the fundamental group $\pi_1(\hbox{\a CP}^2-D)$ for any curve~$D$ in the moduli space ${\cal M}(\{D_{10}+A_5+A_4\},6)$. As an application, we give a new Zariski $4$-ple.

1111 -- 056, 16:30 -- 18:00

Óc Y (ww@Ȋw)

XyNg̑ɂ

ManolescuɂSeiberg-Witten Floerzgs[^ b_1=0,1̂Rspin^cl̂ɑ΂ẴXyNgƂ ꂽDb_1>1̏ꍇɂ̓XyNg̑Ƒz肳D ĈƂwiɕKvȃj@[X̑˂錻ۂ ĎۂD

1118 -- 056, 16:30 -- 18:00

Urs Frauenfelder (kCww@w)

Moment Floer homology and the Arnold-Givental conjecture

We prove the Arnold-Givental conjecture for some class of Lagrangians in Marsden-Weinstein quotients, which are fixpoint sets of some antisymplectic involution. Due to the bubbling phenomenon Floer homology for these Lagrangians cannot be defined by standard means. To overcome this problem we define moment Floer homology. In moment Floer homology the boundary operator is defined by counting solutions of the symplectic vortex equations instead of the Floer equation. The symplectic vortex equations contain an equivariant version of Floer's equation and a condition which relates the curvature to the moment map. The advantage of the symplectic vortex equations is that the relevant moduli spaces are compact, so that the boundary operator can be defined. We prove that moment Floer homology is isomorphic to the singular homology of the Lagrangian with coefficients in some Novikov ring. As Corollary of this result, the Arnold-Givental conjecture for these Lagrangians follows.

1125 -- 056, 16:30 -- 18:00

Gael Meigniez (Univ. de Bretagne Sud)

Making foliated manifolds with prescribed dynamics

Abstract: the transverse dynamics of any codimension one, taut, foliated manifold is represented by a family of diffeomorphisms between subintervals of the circle, called a pseudogroup. We shall reciprocally realize "every" pseudogroup by a taut foliated closed 3-manifold; and discuss some more natural way to change a taut foliated n-manifold for a lower dimensionnal one without changing the dynamics.

122 -- 056, 16:30 -- 18:00

g (ww@Ȋw)

Real K3 surfaces without real points, equivariant determinant of the Laplacian, and the Borcherds Phi-function

̏ꂽ_Ȃ K3 Ȗʂɑ΂ARicci R Kaehler vʂɊւ郉vVA̓ύs񎮂 Borcherds t@C֐pĕ\B

129 -- 126, 16:30 -- 18:00

Myint Zaw (ww@Ȋw, JSPS)

Slit domain model for moduli space of Riemann surfaces

Let $F$ be a connected, compact (orientable or non-orientable) surface of some genus $g\geq 0$ with a tangent direction $\mathfrak X$ (i.e. a non-zero tangent vector up to positive multiple) specified at some base point $\mathcal O \in F$. To specify a tangent direction amounts to specify a boundary curve. Denote ${\mathfrak M}_{g,1}$ the moduli space of equivalence classes $[F, {\mathfrak X}, {\mathcal O}]$.
We will explain a homeomorphic model of ${\mathfrak M}_{g,1}$; namely the space $P(h,c)$, where $h=2g$, of slit domains of $h$ pairs of horizontal slits in the complex plane $\mathbb C$. The $P=P(h,c)$ is an open manifold embedded in a finite cell complex $\bar{P}$ such that $\bar{P}- P$ is a subcomplex of codimension 1.
Using the slit domain model, we compute the homology groups of the moduli spaces ${\mathfrak M}_{g,1}$ the moduli space of (orientable and non-orientable) Reimann surfaces for small genus. We will explain the homology computation for genus one case. Finally we will explain briefly the computation of homology of hyperelliptic moduli spaces.

1216 -- 056, 17:00 -- 18:00

[J (sww@w)

ΊpWȂǂ̐ireguralizationj 葽̑Ώ̐ۑ{zW[ނ̍\ɂāD

OƕM҂́C̃WCԂ̊{zW[ނ \ɂāCq\Ƒۓɂ@JC ̖ɂẮC̕@݂̂ƁC\ɑΏ̐ ۑ܂܁C{zW[ނ\邱ƂłȂD ƂɃOWl̂ɐ$A_{\infty}$㐔 Ώ̐܂܍\邱ƂłȂD ŋ߁CZ̑ۓ̑xɊւ镽ςƂ邱ƂɂC ̖ł邱Ƃ킩̂łɂ (_珉߂ājD @ɂC|eV$\exp H^*(L)$̃[ɂȂ ƂȂǂƂłD WuƂ͈ꕔd邪C {zW[ނ\Ɋւ镔̓Z~i[ŁC ̎g͂ɏWu`ŏqׂD

16 -- 056, 17:00 -- 18:00

C (Bww@w@)

Cobordism of surfaces embedded in S4

We show that every orientable closed connected surface of genus $g$ embedded in $S^4 = \partial B^5$ bounds a 3-dimensional handlebody of genus $g$ embedded in $B^5$. In the non-orientable case, the same result holds if the normal Euler number vanishes. As a corollary, we show that two orientable surfaces embedded in $S^4$ are cobordant if and only if they have the same genus, and that two non-orientable surfaces are cobordant if and only if their genera and normal Euler numbers coincide with each other. These results will be proved by using spin and $\mathrm{Pin}^-$ structures of the embedded surfaces. We also give an application to the realization of Heegaard decompositions of 3-manifolds in $S^5$.

113 -- 056, 16:30 -- 18:00

Zhiqiang Bao (kw/吔)

Maximum orders of some kinds of finite subgroups in Out Fn

Denote by Fn a rank n free group, and denote by Out Fn its outer automorphism group. We will explain how to represent the finite subgroups of Out Fn as group actions on rank n finite connected graphs. Then with the help of a little topology, we will show how to estimate the maximum order of finite subgroups, finite abelian subgroups, and finite cyclic subgroups of Out Fn, as well as the corresponding diagram.

127 -- 056, 16:30 -- 17:30

] N (ww@Ȋw)

Taut foliations of torus knot complements

g[XіڕԂ͋ȖʑɂȂ邱ƂmĂ邪A̋Ȗʑ̖I \n߂āARachel Roberts̒藝ɂ@ɏ]āAȖʂƃ~l[ Vptauttw\\Btauttw\͕Ԃ̋Eɂ g[X̒PȐ̑ƂȂ邪ACӂ̃g[Xіڂɑ΂Ă̒P slope$(-\infty,1)$͈̔͂ŔCӂɎ悤tauttw\\ł邱 ƂؖBĔCӂ̃g[Xіڂɑ΂A͈̔͂slopeɂDehn pē3l̂ɂtauttw\݂邱Ƃ킩B3 l̂tauttw\݂ƁȂl̂͊ŁA{QQƂȂA Ք핢Ԃ$\mathbb{R}^3$ƂȂ邱ƂmĂBɂ̍\ iteratedg[Xіڂɂp邱ƂłB܂ARachel Roberts̍\ ݖڂɑ΂ĂIɊgB

213() -- 056, 16:30 -- 18:00

X FV (_HwHw)

ȖʑL2-sϗʂɂ

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