Frankhuizen, Robin (2017) A∞-resolutions and Massey products on Koszul homology. University of Southampton, Doctoral Thesis, 122pp.
Abstract
This work presents a new approach to studying Massey products on Koszul homology and the Golod property using A∞-algebras. In the first part we study rooted monomial rings which includes monomial rings whose Lyubeznik resolution is minimal. We give a combinatorial characterization of the Golod property for this class of monomial rings. In the second part of this thesis we combine our approach with the power of algebraic Morse theory. In this way, we extend our approach to simplicially resolvable rings, that is, rings with minimal simplicial resolution. We show that for simplicially resolvable rings the Golod property is equivalent to the gcd condition. Lastly, we use our tools to give sufficient conditions for the existence of non-trivial Massey products in low degrees.
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- Faculties (pre 2018 reorg) > Faculty of Social, Human and Mathematical Sciences (pre 2018 reorg) > Mathematical Sciences (pre 2018 reorg)
Current Faculties > Faculty of Social Sciences > School of Mathematical Sciences > Mathematical Sciences (pre 2018 reorg)
School of Mathematical Sciences > Mathematical Sciences (pre 2018 reorg)
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