TL;DR
This paper interprets the cohomology of arithmetically defined groups through lattices, simplifying proofs of their connection to genus and cohomology.
Contribution
It introduces a lattice-based interpretation of group cohomology, providing a more straightforward proof of the genus-cohomology relationship.
Findings
Cohomology can be viewed as equivalence classes of lattices.
Simplifies the proof of the genus-cohomology connection.
Provides new insights into the structure of arithmetically defined groups.
Abstract
We give an interpretation of the cohomology of an arithmetically defined group as a set of equivalence classes of lattices. We use this interpretation to give a simpler proof of the connection established by J. Rohlfs between genus and cohomology.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research