2020N6 -- 7
[English]   [ߋ̃vO]

17:00 -- 18:00 Zoom ł̃ICJ

Last updated September 10, 2020
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623 -- Zoom ł̃ICJ, 17:00 -- 18:00

kl (ww@Ȋw)

Gauge theory and the diffeomorphism and homeomorphism groups of 4-manifolds

Abstract: I will explain my recent collaboration with several groups that develops gauge theory for families to extract difference between the diffeomorphism groups and the homeomorphism groups of 4-manifolds. After Donaldsonfs celebrated diagonalization theorem, gauge theory has given strong constraints on the topology of smooth 4-manifolds. Combining such constraints with Freedmanfs theory, one may find many non-smoothable topological 4-manifolds. Recently, a family version of this argument was started by T. Kato, N. Nakamura and myself, and soon later it was developed also by D. Baraglia and his collaborating work with myself. More precisely, considering gauge theory for smooth fiber bundles of 4-manifolds, they obtained some constraints on the topology of smooth 4-manifold bundles. Using such constraints, they detected non-smoothable topological fiber bundles of smooth 4-manifolds. The existence of such bundles implies that there is homotopical difference between the diffeomorphism and homeomorphism groups of the 4-manifolds given as the fibers. If time permits, I will also mention my collaboration with Baraglia which shows that a K3 surface gives a counterexample to the Nielsen realization problem in dimension 4. This example reveals also that there is difference between the Nielsen realization problems asked in the smooth category and the topological category.
630 -- Zoom ł̃ICJ, 17:00 -- 18:00

Daniel Matei (IMAR Bucharest)

Homology of right-angled Artin kernels

Abstract: The right-angled Artin groups A(G) are the finitely presented groups associated to a finite simplicial graph G=(V,E), which are generated by the vertices V satisfying commutator relations vw=wv for every edge vw in E. An Artin kernel Nh(G) is defined by an epimorphism h of A(G) onto the integers. In this talk, we discuss the module structure over the Laurent polynomial ring of the homology groups of Nh(G).

77 -- Zoom ł̃ICJ, 17:00 -- 18:00

Y (Lw)

Abelian quotients of the Y-filtration on the homology cylinders via the LMO functor

Abstract: We construct a series of homomorphisms on the Y-filtration on the homology cylinders via the mod \$_mathbb{Z}\$ reduction of the LMO functor. The restriction of our homomorphism to the lower central series of the Torelli group does not factor through Morita's refinement of the Johnson homomorphism. We use it to show that the abelianization of the Johnson kernel of a closed surface has torsion elements. This is the joint work with Masatoshi Sato and Masaaki Suzuki.
714 [LieQ_E\_Z~i[ƍ] -- Zoom ł̃ICJ, 17:30 -- 18:30

c K (Lw)

Kobayashi's properness criterion and totally geodesic submanifolds in locally symmetric spaces

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721 -- Zoom ł̃ICJ, 17:00 -- 18:00

Sergei Burkin (ww@Ȋw)

Twisted arrow categories of operads and Segal conditions

Abstract: We generalize twisted arrow category construction from categories to operads, and show that several important categories, including the simplex category Δ, Segal's category Γ and Moerdijk--Weiss category Ω are twisted arrow categories of operads. Twisted arrow categories of operads are closely connected with Segal conditions, and the corresponding theory can be generalized from multi-object associative algebras (i.e. categories) to multi-object P-algebras for reasonably nice operads P.

18:00 -- 19:00

Dexie Lin (ww@Ȋw)

Monopole Floer homology for codimension-3 Riemannian foliation

Abstract: In this paper, we give a systematic study of Seiberg-Witten theory on closed oriented manifold with codimension-3 oriented Riemannian foliation. Under a certain topological condition, we construct the basic monopole Floer homologies for a transverse spinc structure with a bundle-like metric, generic perturbation and a complete local system. We will show that these homologies are independent of the bundle-like metric and generic perturbation. The major difference between the basic monopole Floer homologies and the ones on manifolds is the necessity to use the complete local system to construct the monopole Floer homologies.

728 -- Zoom ł̃ICJ, 17:00 -- 18:00

Anderson Vera (sw͌)

A double filtration for the mapping class group and the Goeritz group of the sphere

Abstract: I will talk about a double-indexed filtration of the mapping class group and of the Goeritz group of the sphere, the latter is the group of isotopy classes of self-homeomorphisms of the 3-sphere which preserves the standard Heegaard splitting of S3. In particular I will explain how this double filtration allows to write the Torelli group as a product of some subgroups of the mapping class group. A similar study could be done for the group of automorphisms of a free group. (work in progress with K. Habiro)