Finite domination and Novikov rings. Laurent polynomial rings in several variables

Thomas Huettemann; David Quinn

doi:10.1016/j.jpaa.2015.12.004

Finite domination and Novikov rings. Laurent polynomial rings in several variables

Thomas Huettemann, David Quinn

Research output: Contribution to journal › Article › peer-review

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Abstract

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.

Original language	English
Pages (from-to)	2648-2682
Number of pages	35
Journal	Journal of Pure and Applied Algebra
Volume	220
Issue number	7
Early online date	12 Jan 2016
DOIs	https://doi.org/10.1016/j.jpaa.2015.12.004
Publication status	Published - Jul 2016

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jpaa.2015.12.004

Finite domination and Novikov rings. Laurent polynomial rings in several variables
©2016 Elsevier Ltd. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ which permits distribution and reproduction for non-commercial purposes, provided the author and source are cited.
Accepted author manuscript, 545 KBLicence: CC BY-NC-ND

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1 Active

R1052PMR: Toric methods in homotopy theory
Huettemann, T.
01/08/2009 → 17/12/2019
Project: Research

2 Invited talk
2 Oral presentation
1 Invited or keynote talk at national or international conference

The algebraic theory of finite domination
Thomas Huettemann (Invited speaker)
21 Jan 2019
Activity: Talk or presentation types › Invited or keynote talk at national or international conference
Toric varieties, Novikov homology and finiteness conditions for chain complexes
Thomas Huettemann (Speaker) & Silvia Sabatini (Organiser)
11 Jul 2018
Activity: Talk or presentation types › Oral presentation
Pure Mathematics Colloquium, Durham (UK): Cubes of chain complexes, multi-complexes and totalisation
Thomas Huettemann (Speaker)
27 Oct 2014
Activity: Talk or presentation types › Invited talk

Thomas Huettemann
- t.huettemann@qub.ac.uk
- School of Mathematics and Physics - Senior Lecturer
- Mathematical Sciences Research Centre
Person: Academic

Cite this

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title = "Finite domination and Novikov rings. Laurent polynomial rings in several variables",

abstract = "We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies. ",

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AB - We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.

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JF - Journal of Pure and Applied Algebra

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Finite domination and Novikov rings. Laurent polynomial rings in several variables

Abstract

ASJC Scopus subject areas

Access to Document

R1052PMR: Toric methods in homotopy theory

The algebraic theory of finite domination

Toric varieties, Novikov homology and finiteness conditions for chain complexes

Pure Mathematics Colloquium, Durham (UK): Cubes of chain complexes, multi-complexes and totalisation

Thomas Huettemann

Cite this