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Title: Functorial Homotopy Decompositions of Iterated Loop Suspensions
Keywords: interated loop suspensions, Snaith splitting, functorial homotopy decomposition
Issue Date: 21-Aug-2014
Source: YUAN ZIHONG (2014-08-21). Functorial Homotopy Decompositions of Iterated Loop Suspensions. ScholarBank@NUS Repository.
Abstract: In this thesis, the problem of functorial homotopy decompositions of iterated loop suspensions is investigated. Due to the complexity of its algebraic structure, the functorial homotopy decomposition of iterated loop suspensions is generally a difficult problem, and few methods have been proposed. Motivated by the ideas and methods developed in functorial homotopy decompositions of the single loop suspension, we first construct a collection of functorial retracts of iterated loop suspensions from a natural coalgebra-split sub-Hopf algebra of tensor algebra. Then the homology groups of these retracts are computed. Finally, we study the Snaith splittings of the functorial retracts we constructed.
Appears in Collections:Ph.D Theses (Open)

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