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- Title
A NOTE ON RATIONAL HOMOLOGICAL STABILITY OF AUTOMORPHISMS OF MANIFOLDS.
- Authors
Krannich, Manuel
- Abstract
By work of Berglund and Madsen, the rings of rational characteristic classes of fibrations and smooth block bundles with fibre |$D^{2n}\sharp (S^n\times S^n)^{\sharp g}$| , relative to the boundary, are for |$2n\ge 6$| independent of |$g$| in degrees |$*\le (g-6)/2$|. In this note, we explain how this range can be improved to |$*\le g-2$| using cohomological vanishing results due to Borel and the classical invariant theory. This implies that the analogous ring for smooth bundles is independent of |$g$| in the same range, provided the degree is small compared to the dimension.
- Subjects
MANIFOLDS (Mathematics); FIBERS
- Publication
Quarterly Journal of Mathematics, 2020, Vol 71, Issue 3, p1069
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmathj/haaa017