Dalian notes on rational Pontryagin classes

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.

v2: corrections in appendix A, references added. v3: new appendix B. v4: bibliography updated, appendix A downsized, typos corrected. v5: abstract added. v6: details added. v7: section 2 simplified, minor mistakes corrected. v8: new fonts, erroneous crossrefs corrected. This will be published under another title, "Rational Pontryagin classes of Euclidean fiber bundles"

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• Spaces of smooth embeddings and configuration categories
• Multiple disjunction for spaces of smooth embeddings
• Some finiteness results for groups of automorphisms of manifolds
• The non-multiplicativity of the signature modulo 8 of a fibre bundle is an Arf-Kervaire invariant
• Truncated operads and simplicial spaces
• Occupants in simplicial complexes

Cited by in corpus (5)

• Embedding calculus and smooth structures
• A spectral sequence for spaces of maps between operads
• Algebraic independence of topological Pontryagin classes
• On automorphisms of high-dimensional solid tori
• The Disc-structure space