Properties of cellular classes of chain complexes
Jonas Kiessling
TL;DR
This paper investigates properties of cellular and acyclic classes of chain complexes over commutative Noetherian rings, establishing that certain shifts of homology modules also belong to these classes.
Contribution
It proves that for finite complexes in a cellular class, all their homology shifts are also contained in the class, revealing a key structural property.
Findings
Shifts of homology modules remain in the cellular class
Finite complexes in a cellular class have stable shifted homology
Provides foundational properties of cellular classes over Noetherian rings
Abstract
In this paper we prove certain properties of cellular and acyclic classes of chain complexes of modules over a commutative Noetherian ring. In particular we show that if X is finite and belongs to some cellular class C then \Sigma^n H_X also belongs to C, for every n.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Geometry