Tuesday Seminar on Topology (October, 2013 -- January, 2014)

[Japanese]   [Past Programs]
16:30 -- 18:00 Graduate School of Mathematical Sciences, The University of Tokyo
Tea: 16:00 -- 16:30 Common Room

Last updated January 8, 2014
Information :　
Toshitake Kohno
Nariya Kawazumi

October 1 -- Room 056, 16:30 -- 18:00

Naoyuki Monden (Tokyo University of Science)

The geography problem of Lefschetz fibrations

Abstract: To consider holomorphic fibrations complex surfaces over complex curves and Lefschetz fibrations over surfaces is one method for the study of complex surfaces of general type and symplectic 4-manifods, respectively. In this talk, by comparing the geography problem of relatively minimal holomorphic fibrations with that of relatively minimal Lefschetz fibrations (i.e., the characterization of pairs (x,y) of certain invariants x and ycorresponding to relatively minimal holomorphic fibrations and relatively minimal Lefschetz fibrations), we observe the difference between complex surfaces of general type and symplectic 4-manifolds. In particular, we construct Lefschetz fibrations violating the "slope inequality" which holds for any relatively minimal holomorphic fibrations.

October 8 -- Room 056, 16:30 -- 18:00

Tatsuro Shimizu (The Univesity of Tokyo)

An invariant of rational homology 3-spheres via vector fields.

Abstract: In this talk, we define an invariant of rational homology 3-spheres with values in a space $\mathcal A(\emptyset)$ of Jacobi diagrams by using vector fields. The construction of our invariant is a generalization of both that of the Kontsevich-Kuperberg-Thurston invariant $z^{KKT}$ and that of Fukaya and Watanabe's Morse homotopy invariant $z^{FW}$. As an application of our invariant, we prove that $z^{KKT}=z^{FW}$ for integral homology 3-spheres.

October 15 -- Room 056, 16:30 -- 18:00

Masamichi Takase (Seikei University)

Desingularizing special generic maps

Abstract: This is a joint work with Osamu Saeki (IMI, Kyushu University). A special generic map is a generic map which has only definite fold as its singularities. We study the condition for a special generic map from a closed n-manifold to the p-space (n+1>p), to factor through a codimension one immersion (or an embedding). In particular, for the cases where p = 1 and 2 we obtain complete results. Our techniques are related to Smale-Hirsch theory, topology of the space of immersions, relation between the space of topological immersions and that of smooth immersions, sphere eversions, differentiable structures of homotopy spheres, diffeomorphism group of spheres, free group actions on the sphere, etc.

October 22 -- Room 056, 16:30 -- 18:00

Rei Inoue (Chiba University)

Cluster algebra and complex volume of knots

Abstract: The cluster algebra was introduced by Fomin and Zelevinsky around 2000. The characteristic operation in the algebra called 'mutation' is related to various notions in mathematics and mathematical physics. In this talk I review a basics of the cluster algebra, and introduce its application to study the complex volume of knot complements in S3. Here a mutation corresponds to an ideal tetrahedron. This talk is based on joint work with Kazuhiro Hikami (Kyushu University).

October 29 -- Room 056, 16:30 -- 18:00

Daniel Matei (IMAR, Bucharest)

Fundamental groups of algebraic varieties

Abstract: We discuss restrictions imposed by the complex structure on fundamental groups of quasi-projective algebraic varieties with mild singularities. We investigate quasi-projectivity of various geometric classes of finitely presented groups.

November 5 -- Room 123, 16:30 -- 18:00

Carlos Moraga Ferrándiz (The University of Tokyo, JSPS)

The isotopy problem of non-singular closed 1-forms.

Abstract: Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class. A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.
The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.

November 12 -- Room 056, 16:30 -- 18:00

Alexander Voronov (University of Minnesota)

The Batalin-Vilkovisky Formalism and Cohomology of Moduli Spaces

Abstract: We use the Batalin-Vilkovisky formalism to give a new proof of Costello's theorem on the existence and uniqueness of solution to the Quantum Master Equation. We also make a physically motivated conjecture on the rational homology of moduli spaces. This is a joint work with Domenico D'Alessandro.

November 19 -- Room 056, 16:30 -- 18:00

Hiroki Kodama (The University of Tokyo)

Minimal C1-diffeomorphisms of the circle which admit measurable fundamental domains

Abstract: We construct, for each irrational number α, a minimal C1-diffeomorphism of the circle with rotation number α which admits a measurable fundamental domain with respect to the Lebesgue measure.
This is a joint work with Shigenori Matsumoto (Nihon University).

November 26 -- Room 056, 16:30 -- 18:00

Hiroo Tokunaga (Tokyo Metropolitan University)

Rational elliptic surfaces and certain line-conic arrangements

Abstract: 　Let S be a rational elliptic surface. The generic fiber of S can be considered as an elliptic curve over the rational function field of one variable. We can make use of its group structure in order to cook up a curve C_2 on S from a given section C_1.
　In this talk, we consider certain line-conic arrangements of degree 7 based on this method.

December 3 -- Room 056, 17:00 -- 18:00

Bruno Martelli (Università di Pisa)

Hyperbolic four-manifolds with one cusp

Abstract: (joint work with A. Kolpakov)
We introduce a simple algorithm which transforms every four-dimensional cubulation into a cusped finite-volume hyperbolic four-manifold. Combinatorially distinct cubulations give rise to topologically distinct manifolds. Using this algorithm we construct the first examples of finite-volume hyperbolic four-manifolds with one cusp. More generally, we show that the number of k-cusped hyperbolic four-manifolds with volume smaller than V grows like C^{V log V} for any fixed k. As a corollary, we deduce that the 3-torus bounds geometrically a hyperbolic manifold.

The talk by Martelli was cancelled.


December 10 -- Room 056, 16:30 -- 18:00

Motoo Tange (University of Tsukuba)

Corks, plugs, and local moves of 4-manifolds.

Abstract: Akbulut and Yasui defined cork, and plug to produce many exotic pairs. In this talk, we introduce a plug with respect to Fintushel-Stern's knot surgery or more 4-dimensional local moves and and argue by using Heegaard Fleor theory.

December 17 -- Room 056, 16:30 -- 18:00

Inasa Nakamura (The University of Tokyo)

Satellites of an oriented surface link and their local moves

Abstract: For an oriented surface link F in R4, we consider a satellite construction of a surface link, called a 2-dimensional braid over F, which is in the form of a covering over F. We introduce the notion of an m-chart on a surface diagram p(F) &sub R3 of F, which is a finite graph on p(F) satisfying certain conditions and is an extended notion of an m-chart on a 2-disk presenting a surface braid. A 2-dimensional braid over F is presented by an m-chart on p(F). It is known that two surface links are equivalent if and only if their surface diagrams are related by a finite sequence of ambient isotopies of R3 and local moves called Roseman moves. We show that Roseman moves for surface diagrams with m-charts can be well-defined. Further, we give some applications.

December 24 -- Room 056, 16:30 -- 18:00

Tirasan Khandhawit (Kavli IPMU)

Stable homotopy type for monopole Floer homology

Abstract: In this talk, I will try to give an overview of the construction of stable homotopy type for monopole Floer homology. The construction associates a stable homotopy object to 3-manifolds, which will recover the Floer groups by appropriate homology theory. The main ingredients are finite dimensional approximation technique and Conley index theory. In addition, I will demonstrate construction for certain 3-manifolds such as the 3-torus.

January 14 -- Room 056, 17:00 -- 18:00

Rinat Kashaev (University of Geneva)

State-integral partition functions on shaped triangulations

Abstract: Quantum Teichmüller theory can be promoted to a generalized TQFT within the combinatorial framework of shaped triangulations with the tetrahedral weight functions given in terms of the Weil-Gelfand-Zak transformation of Faddeev.FN"s quantum dilogarithm. By using simple examples, I will illustrate the connection of this theory with the hyperbolic geometry in three dimensions.

January 21 -- Room 056

16:30 -- 17:30

Naohiko Kasuya (The University of Tokyo)

On contact submanifolds of the odd dimensional Euclidean space

Abstract: We prove that the Chern class of a closed contact manifold is an obstruction for codimension two contact embeddings in the odd dimensional Euclidean space. By Gromov's h-principle, for any closed contact 3-manifold with trivial first Chern class, there is a contact structure on R5 which admits a contact embedding.

17:30 -- 18:30

Xiaolong Li (The University of Tokyo)

Weak eigenvalues in homoclinic classes: perturbations from saddles with small angles

Abstract: For 3-dimensional homoclinic classes of saddles with index 2, a new sufficient condition for creating weak contracting eigenvalues is provided. Our perturbation makes use of small angles between stable and unstable subspaces of saddles. In particular, by recovering the unstable eigenvector, we can designate that the newly created weak eigenvalue is contracting. As applications, we obtain C1-generic non-trivial index- intervals of homoclinic classes and the C1-approximation of robust heterodimensional cycles. In particular, this sufficient condition is satisfied by a substantial class of saddles with homoclinic tangencies.