TORIC TOPOLOGY
WORK SHOP 2016












DATE     11 APRIL 2016

VENUE   ROOM F405, SCIENCE BUILDING F, OSAKA CITY UNIVERSITY



















DESCRIPTION

SUPPORT : JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers "Mathematical Science of Symmetry, Topology and Moduli, Evolution of International Research Network based on OCAMI"

RELATED CONFERENCE : There will be "Toric Topology 2016 in Kagoshima" from 19 to 22 April in Kagoshima.

ORGANIZERS : Mikiya Masuda (Osaka City Univ), Daisuke Kishimoto (Kyoto Univ)







PROGRAM

11 APRIL
10:00〜10:40 Yusuke Suyama (Osaka City Univ)
Toric Fano varieties associated to finite simple graphs
11:00〜12:00 Sho Hasui (Kyoto Univ)
On the p-local stable cohomological rigidity of quasitoric manifolds
13:30〜14:10 Daisuke Kishimoto (Kyoto Univ)
Homotopy decomposition of diagonal arrangements
14:30〜15:30 Ivan Limonchenko (Moscow State Univ)
Moment-angle-manifolds of some 2-truncated cubes and Massey operations
15:50〜16:50 Taras Panov (Moscow State Univ)
Loops on moment-angle complexes and polyhedral products: homotopy decompositions and higher Whitehead brackets
17:10〜18:10 Victor Buchstaber (Moscow State Univ)
Quasitoric 6-dimensional manifold









ABSTRACT

Yusuke Suyama   Toric Fano varieties associated to finite simple graphs

We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a finite simple graph to be Fano or weak Fano in terms of the graph.

Sho Hasui   On the p-local stable cohomological rigidity of quasitoric manifolds

Quasitoric manifolds are a topological generalization of projective non-singular toric varieties, which are 2n-dimensional closed smooth manifolds with good actions of (S1)n. Mikiya Masuda posed the cohomological rigidity problem for quasitoric manifolds, which asks whether or not two quasitoric manifolds with isomorphic cohomology rings are homeomorphic. In this talk we consider a p-local and stable version of this problem. This is a joint work with Daisuke Kishimoto (Kyoto University).

Daisuke Kishimoto   Homotopy decomposition of diagonal arrangements

A diagonal arrangement is a subspace arrangement defined by a simplicial complex and is a generalization of the braid arrangement. I will explain a homotopy decomposition of the suspension of the union of the diagonal arrangement in connection with a polyhedral product. This is a joint work with Kouyemon Iriye.

Ivan Limonchenko   Moment-angle-manifolds of some 2-truncated cubes and Massey operations

Here is the abstract.

Taras Panov   Loops on moment-angle complexes and polyhedral products: homotopy decompositions and higher Whitehead brackets

The polyhedral product is defined as a colimit of a diagram in TOP over the face category of a simplicial complex K. There is a parallel construction of topological groups, called the graph product, defined as a colimit in TGRP and depending only on the 1-skeleton of K. The two constructions can be related by the classifying space functor B and the loop functor Ω. When K is a flag complex, the classifying space of a graph product is the corresponding polyhedral product, and the loops on a polyhedral product is the corresponding graph product. This is not the case when K is not flag; the presence of higher Whitehead brackets obstructs the functors B and Ω to preserve colimits. They do preserve homotopy colimits though, in respective categories TGRP and TOP, which leads to a homotopy decomposition of loops on a polyhedral product XK. A closer look on higher Whitehead brackets leads to some interesting observation on the structure of the loops space on polyhedral products XK and moment-angle complexes ZK=(D2,S1)K In particular, we prove that when ZK is a wedge of spheres, each sphere in the wedge is a lift of an iterated higher Whitehead bracket of the canonical 2-spheres in (CP)K. This should be generalisable to arbitrary polyhedral products of the form (X,A)K. (The latter part is joint with Jelena Grbic.)

Victor Buchstaber   Quasitoric 6-dimensional manifold

Here is the abstract.