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A∞-resolutions and Massey products on Koszul homology

A∞-resolutions and Massey products on Koszul homology
A∞-resolutions and Massey products on Koszul homology
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.
University of Southampton
Frankhuizen, Robin
2d427a81-9d59-49a1-925c-1113027d118f
Frankhuizen, Robin
2d427a81-9d59-49a1-925c-1113027d118f
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175

Frankhuizen, Robin (2017) A∞-resolutions and Massey products on Koszul homology. University of Southampton, Doctoral Thesis, 122pp.

Record type: Thesis (Doctoral)

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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Published date: 1 December 2017

Identifiers

Local EPrints ID: 418265
URI: http://eprints.soton.ac.uk/id/eprint/418265
PURE UUID: d077e873-a7f5-4786-8fcf-b95559a851c6
ORCID for Jelena Grbic: ORCID iD orcid.org/0000-0002-7164-540X

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Date deposited: 27 Feb 2018 17:30
Last modified: 31 Jul 2019 00:34

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