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Full-Text Articles in Physical Sciences and Mathematics
The Fine Structure Of The Kasparov Groups I: Continuity Of The Kk-Pairing, Claude Schochet
The Fine Structure Of The Kasparov Groups I: Continuity Of The Kk-Pairing, Claude Schochet
Mathematics Faculty Research Publications
In this paper it is demonstrated that the Kasparov pairing is continuous with respect to the natural topology on the Kasparov groups, so that a KK-equivalence is an isomorphism of topological groups. In addition, we demonstrate that the groups have a natural pseudopolonais structure, and we prove that various KK-structural maps are continuous.
Extended Powers Of Manifolds And The Adams Spectral Sequence, Robert R. Bruner
Extended Powers Of Manifolds And The Adams Spectral Sequence, Robert R. Bruner
Mathematics Faculty Research Publications
The extended power construction can be used to create new framed manifolds out of old. We show here how to compute the effect of such operations in the Adams spectral sequence, extending partial results of Milgram and the author. This gives the simplest method of proving that Jones’ 30-manifold has Kervaire invariant one, and allows the construction of manifolds representing Mahowald’s classes η4 and η5, among others.