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

Last updated January 21, 2007
bW@
͖r
͐

1010 -- 056, 16:30 -- 18:00

Elmar Vogt (BerlinRw)

Estimating Lusternik-Schnirelmann Category for Foliations: A Survey of Available Techniques

Abstract: The Lusternik-Schnirelmann category of a space $X$ is the smallest number $r$ such that $X$ can be covered by $r + 1$ open sets which are contractible in $X$. For foliated manifolds there are several notions generalizing this concept, all of them due to Helen Colman. We are mostly concerned with the concept of tangential Lusternik-Schnirelmann category (tangential LS-category). Here one requires a covering by open sets $U$ with the following property. There is a leafwise homotopy starting with the inclusion of $U$ and ending in a map that throws for each leaf $F$ of the foliation each component of $U \cap F$ onto a single point. A leafwise homotopy is a homotopy moving points only inside leaves. Rather than presenting the still very few results obtained about the LS category of foliations, we survey techniques, mostly quite elementary, to estimate the tangential LS-category from below and above.

1017 -- 056, 16:30 -- 18:00

Arnaud Deruelle (ww@Ȋwȁj

Networking Seifert Fibered Surgeries on Knots (joint work with Katura Miyazaki and Kimihiko Motegi)

Abstract: We define a Seifert Surgery Network which consists of integral Dehn surgeries on knots yielding Seifert fiber spaces; here we allow Seifert fiber space with a fiber of index zero as degenerate cases. Then we establish some fundamental properties of the network. Using the notion of the network, we will clarify relationships among known Seifert surgeries. In particular, we demonstrate that many Seifert surgeries are closely connected to those on torus knots in Seifert Surgery Network. Our study suggests that the network enables us to make a global picture of Seifert surgeries.@

1024 -- 056, 16:30 -- 18:00

Marco Zunino@(ww@ȊwȁCJSPSj

A review of crossed G-structures

Abstract: We present the definition of "crossed structures" as introduced by Turaev and others a few years ago. One of the original motivations in the introduction of these structures and of the related notion of a "Homotopy Quantum Field Theory" (HQFT) was the extension of Reshetikhin-Turaev invariants to the case of flat principal bundles on 3-manifolds. We resume both this aspect of the theory and other applications in both algebra and topology and we present our results on the algebraic structures involved.

1031 -- 056, 16:30 -- 18:00

MT@(ww@Ȋwȁj

Unsmoothable group actions on elliptic surfaces

Abstract: G ʐ 3, 5, 7 ꂩ̏QƂB {uł͑ȉ~Ȗʏ̋Ǐ^GpŁA̔\ɊւĊ炩ɂȂ Ȃ݂̂邱ƂؖB ߂ɁAQ[W_pāA炩ȍpɑ΂Ă̍S^ B ہASeiberg-Witten sϗʂɑ΂A mod p Œ藝pB ͂ƂF.FangɂĎꂽ藝A􉽓Iȕʏؖɂg邱 Ƃ\łB

1110ij -- 118, 17:40 -- 19:00

aO@ (ww@wnȁ@)

WRT invariant for Seifert manifolds and modular forms

Abstract: We study the SU(2) Witten-Reshetikhin-Turaev invariant for Seifert manifold. We disuss a relationship with the Eichler integral of half-integral modular form and Ramanujan mock theta functions.

1114 -- 056, 16:30 -- 18:00

(MBww)

High-codimensional knots spun about manifolds

Abstract: ^ꂽі(Ⴆ3ԓɖߍ܂ꂽ~) ̌і(Ⴆ4ԓɖߍ܂ꂽ)o@ƂāA XsjOƂ삪BXsjO1925NE. ArtinɂēĈȗA lXȌɈʉA]2̌іڂ̌ł͕sȓɂȂĂB ł́A]3ȏ̌і(Ⴆ6ԓɖߍ܂ꂽ3) XsjOgđ錤ЉB

1128 -- 056, 17:00 -- 18:00

H@aYiȑwHwj

핢Ԃ̎RӒ萔Ɛʒ藝

Abstract: l$M$̗^ꂽ$C$̒ iKꂽjSXJ[ȗ̉ƂƁC RӒ萔$Y(M, C)$ƌĂ΂$(M,C)$̋sϗʂD SĂ̋ނɂ킽ďƂƁC RӕsϗʂƌĂ΂$M$̔ʑsϗʂD $(M, C)$̋핢Ԃ̎RӒ萔 Ƃ$Y(M, C)$̊֌W𒲂ׂ邱Ƃ́Ci$Y(M, C) > 0$̏ꍇj Rӕsϗʂ̌ɂďdvł邱Ƃ킩ĂD $Y(M, C) \leq 0$̏ꍇ́C$C$̒XJ[ȗ̈ӐC ̊֌W͗eՂɋ܂D$Y(M, C) > 0$̏ꍇ́C XJ[ȗ̈Ӑ͐ȂCAubin̕ƌĂ΂ $(M, C)$̗L핢ɑ΂LpȌʂmĂD ̍uł́C$(M, C)$̖̂핢ɑ΂ĂAubin̕ ގIʂ邱ƂЉD ܂̏ؖɕKvƂȂCi핢萶j ٓ_QߓIRȑl̂ɑ΂ ʒ藝ЉD

1212 -- 056, 16:30 -- 18:30

Maxim Kazarian (Steklov Math. Institute)

Thom polynomials for maps of curves with isolated singularities (joint with S. Lando)

Abstract: Thom (residual) polynomials in characteristic classes are used in the analysis of geometry of functional spaces. They serve as a tool in description of classes Poincar\'e dual to subvarieties of functions of prescribed types. We give explicit universal expressions for residual polynomials in spaces of functions on complex curves having isolated singularities and multisingularities, in terms of few characteristic classes. These expressions lead to a partial explicit description of a stratification of Hurwitz spaces.

1219 -- 056, 16:30 -- 18:30

\@(ww@Ȋwȁj

іڂ̂ȂԂ̃zW[QPoisson\

Abstract: $\R^n$ i$n>3$j́igjlong knotŜ̂Ȃ$K$̃zW[Aɂ̏Poisson㐔̍\ɂčl@B ܂œʂPoisson㐔̍\mĂAlittle disks operad̍pɊÂĂBЂƂ̒́A$K$ւ̍pɂ̂łBЂƂ́Alittle disks operad̃FCAoperad ɕtHochschild̂ɍp邱Ƃ痈ĂBHochschild̂$H_* (K)$ɎXyNgn$E^1$ɌBȌʂ́APoisson㐔̍\v邱ƂłB Poissonʂ̍ŏ̔񎩖ȗvZAꂪR[h}ɋNȂzW[ނ̗ł邱ƂB

gc @(ww@Ȋwȁj

On projections of pseudo-ribbon sphere-links.

Abstract: Suppose $F$ is an embedded closed surface in $R^4$. We call $F$ a pseudo-ribbon surface link if its projection is an immersion of $F$ into $R^3$ whose self-intersection set $\Gamma(F)$ consists of disjointly embedded circles. H. Aiso classified pseudo-ribbon sphere-knots ($F$ is a sphere.) when $\Gamma(F)$ consists of less than 6 circles. We classify pseudo-ribbon sphere-links when $F$ is two spheres and $\Gamma(F)$ consists of less than 7 circles.

116 -- 056, 16:30 -- 18:30

Tj@(ww@Ȋwȁj

An SO(3)-version of 2-torsion instanton invariants

Abstract: We construct invariants for simply connected, non-spin $4$-manifolds using torsion cohomology classes of moduli spaces of ASD connections on $SO(3)$-bundles. The invariants are $SO(3)$-version of Fintushel-Stern's $2$-torsion instanton invariants. We show that this $SO(3)$-torsion invariant of $2CP^2 \# -CP^2$ is non-trivial, while it is known that any invariants of $2CP^2 \# - CP^2$ coming from the Seiberg-Witten theory are trivial since $2CP^2 \# -CP^2$ has a positive scalar curvature metric.

R ˎi@(ww@Ȋwȁj

On the non-acyclic Reidemeister torsion for knots

Abstract: The Reidemeister torsion is an invariant of a CW-complex and a representation of its fundamental group. We consider the Reidemeister torsion for a knot exterior in a homology three sphere and a representation given by the composition of an SL(2, C)- (or SU(2)-) representation of the knot group and the adjoint action to the Lie algebra. We will see that this invariant is expressed by the differential coefficient of the twisted Alexander invariant of the knot and investigate some properties of the invariant by using this relation.

123 -- 056, 16:30 -- 18:30

c @(ww@Ȋwȁj

ȑo΃cHtCvʂɊւcCX^[Ή ----ِ̓ƊȖ

Abstract: C. LeBrun L. J. Mason , ̓̂̂ɊւăcCX^[^̑Ή 邱ƂĂ. Ȃ킿, (2,2) ̕sl\ł ̏𖞂̂, RP^3 CP^3 ւ̖̂ߍ݂ł. ̍uł, LeBrun Mason ̌ʂ𓥂܂̘bɂĐ.
܂, ̂悤ȋ\łĂtw\̂. nullȖʂɂtw\ł, ِ̓̂ł. ̍\ɊւđIȃcCX^[Ή邱Ƃ, ̑Ή, 鏤Ԃ̊Ԃ̒᎟̑ΉU邱Ƃ.
, \̂̂ɓِ󋵂ɂĈ̒莮^. LeBrun Mason ̒藝ِ̓̂ւ̈ʉ ɂĂ̗\z莮, ɂ̗̋ɂĐ.

On the homology group of $Out(F_n)$

Abstract: Suppose $F_n$ is the free group of rank $n$, $Out(F_n) = Aut(F_n)/Inn(F_n)$ the outer automorphism group of $F_n$. We compute $H_*(Out(F_n);\mathbb{Q})$ for $n\leq 6$ and conclude that non-trivial classes in this range are generated by Morita classes $\mu_i \in H_{4i}(Out(F_{2i+2});\mathbb{Q})$. Also we compute odd primary part of $H^*(Out(F_4);\mathbb{Z})$.

130 -- 056, 16:30 -- 18:00

John F. Duncan (Harvard University)

Elliptic genera and some finite groups

Abstract: Recent developments in the representation theory of sporadic groups suggest new formulations of moonshine' in which Jacobi forms take on the role played by modular forms in the monstrous case. On the other hand, Jacobi forms arise naturally in the study of elliptic genera. We review the use of vertex algebra as a tool for constructing the elliptic genus of a suitable vector bundle, and illustrate connections between this and vertex algebraic representations of certain sporadic simple groups.

ߋ̃vO

To Seminar Information