On the homology of the dual de Rham complex
Roman Mikhailov
TL;DR
This paper investigates the homology of the dual de Rham complex as functors on abelian groups, providing explicit descriptions up to degree 7 for free abelian groups and correcting previous proofs.
Contribution
It offers new explicit homology descriptions for the dual de Rham complex and corrects earlier computational proofs.
Findings
Homology description up to degree 7 for free abelian groups
Corrected proof of Jean's zeroth homology group computation
Enhanced understanding of the dual de Rham complex's homological properties
Abstract
We study the homology of the dual de Rham complex as functors on the category of abelian groups. We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the proof of Jean's computations of the zeroth homology group.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models