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

详细信息    查看全文

• 作者：Thomas Hü ; ttemann^a ; ^{t.huettemann@qub.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; David Quinn^b ; ^{D.Quinn@ed.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 18G35 ; secondary ; 55U15
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：220
• 期：7
• 页码：2648-2682
• 全文大小：634 K

文摘

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.