On the homotopy groups of toric spaces with applications to the homotopy groups of certain manifolds.

Title: On the homotopy groups of toric spaces with applications to the homotopy groups of certain manifolds.
Identifier: AAI3213141
identifier: 3213141
Creator: Allen, David.
Contributor: Adviser: Martin Bendersky
Date: 2006
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: Given an n-dimensional, q-neighborly simple convex polytope P one has the associated borel space, moment angle complex and family of toric manifolds that sit over P. Recently there has been much focus on the homotopy groups and homotopy type of the moment angle complex. Buchstaber and Panov determined the first non-trivial homotopy group of the borel space using a particular cellular structure. In this thesis the notion of relations among relations is put in the unstable BP context. This allows for the determination of R1PBP*(BTP) through a range. The stable and unstable co-action on R 1PBP*(BTP) is computed and shown to coincide with the co-action on a product of spheres whose dimensions depend on the combinatorics of P. As a result, the higher homotopy groups of the borel space can be determined through a range that was previously unknown. Applications to the homotopy type of a family of moment angle complexes will be given.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Media: On the homotopy groups of toric spaces with applications to the homotopy groups of certain manifolds.