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Title: Derived A-infinity algebras : combinatorial models and obstruction theory
Author: Halliwell, Gemma
ISNI:       0000 0004 7233 7681
Awarding Body: University of Sheffield
Current Institution: University of Sheffield
Date of Award: 2017
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Let R be a commutative ring, and let A be a derived A∞-algebra over R with structure maps m_ij for all i ≥ 0, j ≥ 1. In this thesis we construct a collection of based topological spaces V_ij which give rise to the notion of a DA∞-space. The structure of these spaces gives new insight into the structure of a derived A∞-algebra. We study the cell structure of these spaces via a combinatorial model using partitioned trees. We will prove that the singular chain complex on a DA∞-space gives rise to a derived A∞-algebra. We go on to consider obstruction theories to the existence of the structure maps of a derived A∞-algebra. The bigrading on A leads to choices of the order in which we develop the derived A∞-structure. We give three different definitions of a “partial” derived A∞-structure and in light of these definitions provide two different obstruction theories to extend a dA ́_ij-structure to a dA_ij structure, plus an obstruction theory to extend a dA_r-1-structure to a dA_r+1-structure. In each case, the obstruction lies in a particular class of the Hochschild cohomology of the homology of A.
Supervisor: Whitehouse, Sarah Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available