Finite domination and NOVIKOV homology over strongly Z2-graded rings

Thomas Hüttemann*, Luke Steers

*Corresponding author for this work

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Abstract

Let R be a strongly Z2 -graded ring, and let C be a bounded chain complex of finitely generated free R-modules. The complex C is R(0,0)-finitely dominated, or of type FP over R(0,0), if it is chain homotopy equivalent to a bounded complex of finitely generated projective R(0,0)-modules. We show that this happens if and only if C becomes acyclic after taking tensor product with a certain eight rings of formal power series, the graded analogues of classical NOVIKOV rings. This extends results of RANICKI, QUINN and the first author on LAURENT polynomial rings in one and two indeterminates.
Original languageEnglish
Number of pages33
JournalProceedings of the Royal Society of Edinburgh. Section A. Mathematics
Early online date28 Jul 2023
DOIs
Publication statusEarly online date - 28 Jul 2023

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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