Topology Seminar - Homotopy fibrations in toric topology - Xin Fu (Southampton) & Massey products in toric topology - Abi Linton (Southampton) Seminar

Talk 1 Xin Fu - Homotopy fibrations in toric topology

Abstract: Let f:K-->L be a simplicial map between finite simplicial complexes. Then f induces a continuous map g: (S^1, *)^K --> (S^1, *)^L between polyhedral products using the multiplicative structure on S^1. This can be seen as a homotopy theoretical generalisation of the Bestvina- Brady construction.

In this talk, I will consider the homotopy fibre of the map g and in certain cases, describe its homotopy type.

Talk 2 Abi Linton - Massey products in toric topology

Abstract: Massey products are secondary operations defined on differential graded algebras, such as on the cohomology rings of a topological space. Although difficult to describe, there are a number of applications of Massey products in topology, geometry, algebra and combinatorics. For example, a triple Massey product detects the non-trivial linking in the Borromean rings, which cannot be detected by cup products in cohomology.

Toric topology is the study of spaces arising from m-torus actions on topological spaces, whose orbit spaces have a rich combinatorial structure. A key example of such spaces are moment-angle complexes Z_K, whose T^m-orbit space is a simplicial complex K on m-vertices. In this talk, I detect Massey products on moment-angle complexes and describe them in combinatorial terms.