Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.568570 
Title:  The homotopy exponent problem for certain classes of polyhedral products  
Author:  Robinson, Daniel Mark 
ISNI:
0000 0004 2736 8390


Awarding Body:  University of Manchester  
Current Institution:  University of Manchester  
Date of Award:  2012  
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Abstract:  
Given a sequence of n topological pairs (X_i,A_i) for i=1,...,n, and a simplicial complex K, on n vertices, there is a topological space (X,A)^K by a construction of Buchstaber and Panov. Such spaces are called polyhedral products and they generalize the central notion of the momentangle complex in toric topology. We study certain classes of polyhedral products from a homotopy theoretic point of view. The boundary of the 2dimensional nsided polygon, where n is greater than or equal to 3, may be viewed as a 1dimensional simplicial complex with n vertices and n faces which we call the ngon. When K is an ngon for n at least 5, (D^2,S^1)^K is a hyperbolic space, by a theorem of Debongnie. We show that there is an infinite basis of the rational homotopy of the based loop space of (D^2,S^1)^K represented by iterated Samelson products. When K is an ngon, for n at least 3, and P^m(p^r) is a mod p^r Moore space with m at least 3 and r at least 1, we show that the order of the elements in the pprimary torsion component in the homotopy groups of (Cone X, X)^K, where X is the loop space of P^m(p^r), is bounded above by p^{r+1}. This result provides new evidence in support of a conjecture of Moore. Moreover, this bound is the best possible and in fact, if a certain conjecture of M.J Barratt is assumed to be true, then this bound is also valid, and is the best possible, when K is an arbitrary simplicial complex.


Supervisor:  Ray, Nige  Sponsor:  Not available  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.568570  DOI:  Not available  
Keywords:  polyhedral product ; exponent ; homotopy ; moment angle complex ; Moore space ; Moore's Conjecture ; Barratt's Conjecture  
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