Tuesday Seminar on Topology

16:30 -- 18:00 Graduate School of Mathematical Sciences, The University of Tokyo
Tea: 16:00 -- 16:30 Common Room

Last updated June 23, 2006
Information :@
Toshitake Kohno
Nariya Kawazumi

April 11 -- Room 056, 16:30 -- 18:00

Martin Arkowitz (Dartmouth College)

Homotopy actions, cyclic maps and their Eckmann-Hilton duals.

Abstract: We study the homotopy action of a based space A on a based space X. The resulting map A--->X is called cyclic. We classify actions on an H-space which are compatible with the H-structure. In the dual case we study coactions X--->X v B and the resulting cocyclic map X--->B. We relate the cocyclicity of a map to the Lusternik-Schnirelmann category of the map.

April 18 -- Room 056, 16:30 -- 18:00

Vladimir Turaev (Univ. Louis Pasteur Strasbourg)

Topology of words

Abstract: There is a parallel between words, defined as finite sequences of letters, and curves on surfaces. This allows to treat words as geometric objects and to analyze them using techniques from low-dimensional topology. I will discuss basic ideas in this direction and the resulting topological invariants of words.

Monday, April 24 -- Room 056, 15:00 -- 16:00, Special Lecture by Professor Montesinos

Jose Maria Montesinos-Amilibia (Universidad Complutense de Madrid)

Hyperbolic manifolds fibered over S1 in infinitely many different ways

April 25 -- Room 056, 16:30 -- 18:00

Hiroshi Goda (Tokyo University of Agriculture and Technology)

Counting closed orbits and flow lines via Heegaard splittings

Abstract: Let K be a fibred knot in the 3-sphere. It is known that the Alexander polynomial of K is essentially equal to a Lefschetz zeta function obtained from the monodromy map of the fibre structure. In this talk, we discuss the non-fibred knot case. We introduce "monodromy matrix" by making use of Heegaard splitting for sutured manifolds of a knot K, and then observe a method of counting closed orbits and flow lines, which gives the Alexander polynomial of K. This observation is based on works of Donaldson and Mark. (joint work with Hiroshi Matsuda and Andrei Pajitnov)

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

Laurentiu Maxim (University of Illinois at Chicago)

Fundamental groups of complements to complex hypersurfaces

Abstract: I will survey various Alexander-type invariants of hypersurface complements, with an emphasis on obstructions on the type of groups that can arise as fundamental groups of complements to affine hypersurfaces.

May 23 -- Room 056, 16:30 -- 18:00

Ryoji Kasagawa (Nihon University)

On crossed homomorphisms on symplectic mapping class groups

Abstract: We consider a symplectic manifold M. For a relation between Chern classes of M and the cohomology class of the symplectic form, we construct a crossed homomorphism on the symplectomorphism group of M with values in the cohomology group of M. We show an application of it to the flux homomorphism. Then we see that it induces a one on the symplectic mapping class group of M and show a nontrivial example of it.

May 30 -- Room 056, 16:30 -- 18:00

Takao Satoh (University of Tokyo)

On crossed homomorphisms on symplectic mapping class groups

Abstract: In this talk we determine the structure of the cokernel of the Johnson homomorphisms for degree two and three. We also show that restricting the initial domain of the Johnson homomorphisms to the submodule generated by the degree one elements, we can obtain new obstructions for the surjectivity of the Johnson homomorphisms.

June 6 -- Room 056, 16:30 -- 18:00

Shigeaki Miyoshi (Chuo University)

Thurston's inequality for a foliation with Reeb components

Abstract: The Euler class of a Reebless foliation or a tight contact structure on a closed 3-manifold satisfies Thurston's inequality, i.e. its (dual) Thurston norm is less than or equal to 1. It should be significant to study Thurston's inequality in both of foliation theory and contact topology. We investigate conditions for a spinnable foliation one of which assures that Thurston's inequality holds and also another of which implies the violation of the inequality.

June 13 -- Room 056, 16:30 -- 18:00

Kokoro Tanaka (University of Tokyo)

A note on C1-moves

Abstract: S. Kamada introduced the notion of a chart which is a tool for describing a 2-dimensional braid, where a chart is an oriented labelled graph in a 2-disk. He defined moves for charts, called C-moves, which consist of three classes of moves: a C1-move, a C2-move and a C3-move, and proved that there exists a one-to-one correspondence between the equivalence classes of surface braids and the C-move equivalence classes of charts. J. S. Carter and M. Saito proved that any C1-move can be realized by a finite sequence of seven types of elementary C1-moves, but it has been known that there are some ambiguous arguments in their proof. In this talk, we give a precise proof for their assertion by a different approach from theirs. B

June 27 -- Room 056, 16:30 -- 18:00

Cedric Tarquini (Ecole Nomale Superieure of Lyon)

Lorentzian foliations on 3-manifolds

a joint work with C. Boubel (Ecole Nomale Superieure of Lyon) and P. Mounoud (University of Bordeaux 1 sciences and technologies)

Abstract: The aim of this work is to give a classification of transversely Lorentzian one dimensional foliations on compact manifolds of dimension three. There are the foliations which admit a transverse pseudo-Riemanniann metric of index one. It is the Lorentzian analogue of the better known Riemannian foliations and they still have rigid transverse geometry.

The Riemannian case was listed by Y. Carriere and we will see that the Lorentzian one is very different and much more complicated to classify. The difference comes form the fact that the completness of the transverse structure, which is automatic in the Riemannian case, is a very strong hypothesis for a transverse Lorentzian foliation.

We will give a classification of complete Lorentzian foliations and some examples which are not complete. As a natural corollary of this classification we will list the codimension one timelike geodesically complete totally geodesic foliations of Lorentzian compact three manifolds.

July 4 -- Room 056, 16:30 -- 18:00

Alexander A. Ivanov (Imperial College (London))

Amalgams: a machinery of the modern theory of finite groups


July 11 -- Room 056, 17:00 -- 18:30

Takeo NODA (Akita University)

On the existence of total foliations

a joint work with M. Asaoka and E. Dufraine

Abstract: A total foliation on an n-manifold is an n-tuple of codimension one foliations such that the intersection of the tangent spaces of them at each point reduces to 0. It is proved by Hardorp that all compact orientable three dimensional manifolds admit total foliations. For a given total foliation on a 3-manifold, we can easily see that the tangent plane fields of each foliation are homotopic to each other and define a homotopy class of plane field with euler class zero. Then it is natural to ask whether any homotopy class with euler class zero can be realized by a total foliation. In this talk, we will give a positive answer to this question. As an application, we will also mention the existence problem of bi-contact structure, a pair of positive and negative contact structures which intersect transversely.

July 24 (Mon) -- Room 056, 16:30 -- 17:30

Boris Hasselblatt (Tufts University)

Invariant foliations in hyperbolic dynamics: Smoothness and smooth equivalence

Abstract: The stable and unstable leaves of a hyperbolic dynamical system are smooth and form a continuous foliation. Smoothness of this foliation sometimes constrains the topological type of the foliation, other times restricts at least the smooth equivalence class of the dynamical system, or for geodesic flows, the type of the underlying manifold. I will present a broad introduction as well as recent work, work in progress, and open problems.

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