One day seminar in Toric Topology

Đorđe Baralić (Mathematical Institute of the Serbian Academy of Sciences and Arts)

Toric topology of neighborly polytopes [Slide]

Abstract: In this talk we address some new results addressing small covers and quasitoric manifolds over simple neighborly polytopes as well as their Buchstaber number. The problems of cohomological rigidity of these manifolds will be also studied.

Vladislav Cherepanov (Higher School of Economics)

Torus actions of complexity 1 in non-general position and their orbit spaces.

Abstract: In the talk, I intend to outline known results and examples regarding torus actions of complexity one; special attention will be given to the case of actions in non-general position. There will be presented the results of joint work with A. Ayzenberg concerning homology groups of the orbit spaces of such actions.

Ivan Limonchenko (Higher School of Economics)

On moment-angle-complexes of lower Lusternik--Schnirelmann category [Slide]

Abstract: In this talk we relate topological properties of moment-angle-complexes of LS-category not greater than two to algebraic properties of the Stanley--Reisner rings of the underlying simplicial complexes. Relying on the known examples, we state a conjecture describing the case when a moment-angle manifold has LS-category equal to two and give examples which show the conjecture fails for simplicial complexes different from triangulated spheres. The talk is based on joint works in progress with T.Panov and with D.Baralic, J.Grbic, and A.Vucic.

V. Uma (Indian Institute of Technology Madras)

Equivariant K-theory of toric orbifolds [Slide]

Abstract: I shall state some recent results on this topic.

Rade Živaljević (Mathematical Institute of the Serbian Academy Of Sciences And Arts)

Bier spheres and Kantorovich-Rubinstein polytopes of weighted cycles [Slide]

Abstract: The problem of deciding if a given triangulation of a sphere can be realized as the boundary sphere of a simplicial, convex polytope is known as the `Simplicial Steinitz problem'. It is known by an indirect and non-constructive argument that a vast majority of Bier spheres are non-polytopal. Contrary to that, we demonstrate that the Bier spheres associated to threshold simplicial complexes are all polytopal. Moreover, we show that all Bier spheres are starshaped. We also establish a connection between Bier spheres and Kantorovich-Rubinstein polytopes by showing that the boundary sphere of the KR-polytope associated to a polygonal linkage (weighted cycle) is isomorphic to the Bier sphere of the associated simplicial complex of ``short sets''.

Elizaveta Zhuravleva (Moscow State University)

Higher Whitehead products and L-infinity structures in toric topology [Slide]

Abstract: In this talk I discuss higher Whitehead products, invariants in unstable homotopy theory, which are considered in the context of the studying of moment-angle complexes. It is known that rational homotopy groups of loop space form the homotopy Lie algebra in which the Jacobi identity holds. There is a structure of L-infinity algebra, the generalization of Lie algebra for which we have n-ary brackets that satisfy the generalized Jacobi identities. In this talk I represent the connection between higher Whitehead products and L-infinity structures on homotopy Lie algebra in the case of moment-angle complexes.