Andy Tonks in nLab

Andy Tonks is a British mathematicain who works in the Departamento de Álgebra, Geometría y Topología Universidad de Málaga, Málaga, Spain.

• website

Selected writings

On crossed complexes:

• Andrew Tonks: Theory and Applications of Crossed Complexes, PhD thesis, Bangor (1993) [pdf, pdf]

On cohomology of monoids in monoidal categories (specifically in distributive monoidal categories):

• Hans-Joachim Baues, Mamuka Jibladze, Andy Tonks, Cohomology of monoids in monoidal categories, in: Operads: Proceedings of Renaissance Conferences, Contemporary Mathematics 202, AMS (1997) 137-166 [doi:10.1090/conm/202, preprint:pdf]

On the Adams-Hilton model for the Pontrjagin ring-structure on the singular chain complex of a based loop space:

• Kathryn Hess, Paul-Eugène Parent, Jonathan Scott, Andrew Tonks, A canonical enriched Adams-Hilton model for simplicial sets, Advances in Mathematics 207 2 (2006) 847-875 [doi:10.1016/j.aim.2006.01.013, arXiv:math/0408216]

On the Hurewicz theorem for cubical homology:

• Daniel Carranza, Chris Kapulkin, Andrew Tonks: The Hurewicz theorem for cubical homology, Mathematische Zeitschrift 305 61 (2023) [doi:10.1007/s00209-023-03352-0, arXiv:2207.12500]

An indepedent treatment of 2-Segal spaces as decomposition spaces

• Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks, Decomposition spaces, incidence algebras and Möbius inversion, arXiv:1404.3202

See also:

• Andrew P. Tonks, On the Eilenberg-Zilber Theorem for crossed complexes, J. Pure Appl. Algebra, 179~(1-2) (2003) 199–220,

• Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks. Homotopy linear algebra. Proc. Roy. Soc. Edinburgh Sect. A, 148(2):293–325, 2018.

• Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks. Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees, Adv. Math., 254:79–117, 2014.

• Imma Gálvez-Carrillo, Andy Tonks, Bruno Vallette, Homotopy Batalin-Vilkovisky algebras, J. Noncomm. Geom. 6:3, 539–602 arXiv:0907.2246 doi

• Imma Gálvez, Vassily Gorbounov, Andrew Tonks, Homotopy Gerstenhaber structures and vertex algebras, math/0611231.QA

• Eilenberg-Zilber theorem

• homotopy BV-algebra

• 2-Segal space