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

Last updated February 9, 2009
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1014 -- 056, 16:30 -- 18:00

Jeffrey Herschel Giansiracusa (Oxford University)

Pontrjagin-Thom maps and the Deligne-Mumford compactification

Abstract: An embedding f: M -> N produces, via a construction of Pontrjagin-Thom, a map from N to the Thom space of the normal bundle over M. If f is an arbitrary map then one instead gets a map from N to the infinite loop space of the Thom spectrum of the normal bundle of f. We extend this Pontrjagin-Thom construction of wrong-way maps to differentiable stacks and use it to produce interesting maps from the Deligne-Mumford compactification of the moduli space of curves to certain infinite loop spaces. We show that these maps are surjective on mod p homology in a range of degrees. We thus produce large new families of torsion cohomology classes on the Deligne-Mumford compactification.

1021 -- 002, 16:30 -- 18:00

XR NT (ww@Ȋw)

3l̂6l̂ւ̖ߍ݂ɂ

Abstract: 3l̂6l̂ւ̂Ȃ߂炩Ȗߍ݂̕sϗʂ̊ȌȌI^܂D ̌6A3̑l̑΁iɕԂ̂RzW[ނ̏t́j̃R{fBY 4l̂̕sɂpďqׂ܂B ̕sϗʂpĒ᎟g|W[ɂ邢̌ÓTIȕsϗ (Haefliger invariant, Milnor's triple linking number, Rokhlin invariant, Casson invariant, Takase's invariant, Skopenkov's invariants) 𓝈I()\o邱Ƃ֘A邢̉pЉƎv܂B

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

aF (ww@Ȋw)

Nonsmoothable group actions on spin 4-manifolds

Abstract: We call a locally linear group action on a topological manifold nonsmoothable if the action is not smooth with respect to any possible smooth structure. We show in this lecture that every closed, simply connected, spin topological 4-manifold not homeomorphic to S2 x S2 or S4 allows a nonsmoothable group action of any cyclic group with sufficiently large prime order which depends on the manifold.

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

Misha Verbitsky (ITEP, Moscow)

Lefschetz SL(2)-action and cohomology of Kaehler manifolds.

Abstract: Let M be compact Kaehler manifold. It is well known that any Kaehler form generates a Lefschetz SL(2)-triple acting on cohomology of M. This action can be used to compute cohomology of M. If M is a hyperkaehler manifold, of real dimension 4n, then the subalgebra of its cohomology generated by the second cohomology is isomorphic to a polynomial algebra, up to the middle degree.

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

Thomas Andrew Putman (MIT)

The second rational homology group of the moduli space of curves with level structures

Abstract: Let $\Gamma$ be a finite-index subgroup of the mapping class group of a closed genus $g$ surface that contains the Torelli group. For instance, $\Gamma$ can be the level $L$ subgroup or the spin mapping class group. We show that $H_2(\Gamma;\Q) \cong \Q$ for $g \geq 5$. A corollary of this is that the rational Picard groups of the associated finite covers of the moduli space of curves are equal to $\Q$. We also prove analogous results for surface with punctures and boundary components.

1118 -- 056, 17:00 -- 18:00

q L (sww@w)

f͊wn̂肱݂ƍ

Abstract: ɕ򂪏WςĂ悤 ̗͊wnɂẮAԂp[^Ԃ ׍\グX̗͊wn̑ɊȂ ՓI\肷邱ƂmĂA Ӗō̖ƂȂĂB̌ۂ̐ɂ́A 镔Wւ̍ċAʑ̍\瓾ANX ͊wnŜ̋ԂŒ郁^͊wnƂĂ 肱ݍpf̍ldvłBɊւāA u҂ƈ[sɂ钆Is_f͊wn ߕ^肱݂̘b𒆐SɉB

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

Andrei Pajitnov (Université de Nantes)

Circle-valued Morse theory for knots and links

Abstract: We will discuss several recent developments in this theory. In the first part of the talk we prove that the Morse-Novikov number of a knot is less than or equal to twice the tunnel number of the knot, and present consequences of this result. In the second part we report on our joint project with Hiroshi Goda on the half-transversal Morse-Novikov theory for 3-manifolds.

122 -- 056, 17:00 -- 18:00 (LieQ_E\_Z~i[ƍŊJ)

F (ÉwȊw)

Vanishing and Rigidity

Abstract: The aim of my talk is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, andrigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank noncompact Lie group, on the other. The connection is established via "transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1- form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.

129 -- 056, 16:30 -- 18:00

Bertrand Deroin (CNRS, Orsay, Université Paris-Sud 11)

Tits alternative in Diff1(S1)

Abstract: The following form of Tits alternative for subgroups of homeomorphisms of the circle has been proved by Margulis: or the group preserve a probability measure on the circle, or it contains a free subgroup on two generators. We will prove that if the group acts by diffeomorphisms of class C1 and does not preserve a probability measure on the circle, then in fact it contains a subgroup topologically conjugated to a Schottky group. This is a joint work with V. Kleptsyn and A. Navas.

113 -- 002, 16:30 -- 17:30

R (ww@Ȋw)

Ot̓Q̃RpNgɂ

Abstract: Topological properties of homeomorphism groups, especially of finite-dimensional manifolds, have been of interest in the area of infinite-dimensional manifold topology. For a locally finite graph $\Gamma$ with countably many components, the homeomorphism group $\mathcal{H}(\Gamma)$ and its identity component $\mathcal{H}_+(\Gamma)$ are topological groups with respect to the compact-open topology. I will define natural compactifications $\overline{\mathcal{H}}(\Gamma)$ and $\overline{\mathcal{H}}_+(\Gamma)$ of these groups and describe the topological type of the pair $(\overline{\mathcal{H}}_+(\Gamma), \mathcal{H}_+(\Gamma))$ using the data of $\Gamma$. I will also discuss the topological structure of $\overline{\mathcal{H}}(\Gamma)$ where $\Gamma$ is the circle.

120 -- 002, 16:30 -- 17:30

V [ (ww@Ȋw)

K 2 5 $K$ ڐGl̂ɂ

Tv : $K$ ڐGl̂Ƃ́AڐG $\alpha$ l $M$ ł $\alpha$ Reeb $M$ Riemannvʂۂ̂łBႦ΁AXؑl̂̉̐ڐGl̂ $K$ ڐGl̂łBReeb̕ɂ $T^2$ p^ $5$ $K$ ڐGl̂ɑ΂A $T^2$ pɕtڐG^ʎʑMorse_Kē錋ʁipɂ镪ށAK鍲X،vʂ̑݁Ag[bNڐGl̂ɂȂ邽߂̏\jɂďqׂB

17:30 -- 18:30

ɓ썹 (ww@Ȋw)

Surface links which are coverings of a trivial torus knot

Abstract: We consider surface links which are in the form of coverings of a trivial torus knot, which we will call torus-covering-links. By definition, torus-covering-links include spun T2-knots, turned spun T2-knots, and symmetry-spun tori. We see some properties of torus-covering-links.

127 -- 056, 17:00 -- 18:00

[J (sww@w)

OWl̂̃tA[zW[ n~gQ̋[^

Tv : Ggtƃ|erb`̓I[̃XyNgsϗʂp n~gQ̋[^\D ̍uł̓OWl̂̃tA[zW[pāC ̋[^̗lq𒲂ׂD ܂C傫ʎqRzW[ɊÂXyNgsϗʂ ꍇւ̈ʉD pƃg[bNl̂̏ꍇ قȂ鑽̋[^Ⴊ\łD iI[CcC쎁Ƃ̋ɊÂDj

35 () -- 056, 16:30 -- 18:00

Shicheng Wang (Peking University)

Extending surface automorphisms over 4-space

Abstract: Let $e: M^p\to R^{p+2}$ be a co-dimensional 2 smooth embedding from a closed orientable manifold to the Euclidean space and $E_e$ be the subgroup of ${\cal M}_M$, the mapping class group of $M$, whose elements extend over $R^{p+2}$ as self-diffeomorphisms. Then there is a spin structure on $M$ derived from the embedding which is preserved by each $\tau \in E_e$.
Some applications: (1) the index $[{\cal M}_{F_g}:E_e]\geq 2^{2g-1}+2^{g-1}$ for any embedding $e:F_g\to R^4$, where $F_g$ is the surface of genus $g$. (2) $[{\cal M}_{T^p}:E_e]\geq 2^p-1$ for any unknotted embedding $e:T^p\to R^{p+2}$, where $T^p$ is the $p$-dimensional torus. Those two lower bounds are known to be sharp.
This a joint work of Ding-Liu-Wang-Yao.

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