Dalian notes on rational Pontryagin classes
Michael S. Weiss

TL;DR
This paper discusses the behavior of rational Pontryagin classes in fiber bundles with 2n-dimensional Euclidean fibers, highlighting their potential to be nonzero in unexpectedly high cohomology degrees, contrasting with vector bundle cases.
Contribution
It reveals that rational Pontryagin classes can be nonzero in high cohomology degrees for certain fiber bundles, unlike their behavior in vector bundles.
Findings
Pontryagin classes can be nonzero in high cohomology degrees
Contrast with Pontryagin classes of vector bundles
Highlights differences in topological properties
Abstract
The rational Pontryagin classes, evaluated on fiber bundles where the fiber is a 2n-dimensional euclidean space, can be nonzero in cohomology dimensions much greater than 4n. This makes a striking contrast with the Pontryagin classes of vector bundles.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Algebra and Geometry
