Some rational homology computations for diffeomorphisms of odd‐dimensional manifolds Article Swipe
Related Concepts
Mathematics
Diffeomorphism
Cohomology
Pure mathematics
Automorphism
Classifying space
Homotopy
Homology (biology)
Commutative property
Group (periodic table)
Algebra over a field
Block (permutation group theory)
Computation
Combinatorics
Chemistry
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Organic chemistry
Gene
Algorithm
Johannes Ebert
,
Jens Reinhold
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1112/topo.12324
· OA: W4391387438
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1112/topo.12324
· OA: W4391387438
We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds , for large and , up to degree . The answer is that it is a free graded commutative algebra on an appropriate set of Miller–Morita–Mumford classes. Our proof goes through the classical three‐step procedure: (a) compute the cohomology of the homotopy automorphisms, (b) use surgery to compare this to block diffeomorphisms, and (c) use pseudoisotopy theory and algebraic ‐theory to get at actual diffeomorphism groups.
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