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Full-Text Articles in Physical Sciences and Mathematics
Geometric Realization And K-Theoretic Decomposition Of C*-Algebras, Claude Schochet
Geometric Realization And K-Theoretic Decomposition Of C*-Algebras, Claude Schochet
Mathematics Faculty Research Publications
Suppose that A is a separable C*-algebra and that G∗ is a (graded) subgroup of the ℤ/2-graded group K∗(A). Then there is a natural short exact sequence
0 → G∗ → K∗(A) → K∗(A)/G∗ → 0.
In this note we demonstrate how to geometrically realize this sequence at the level of C*-algebras. As a result, we KK-theoretically decompose A as
0 → A ⊗ [cursive]K → Aƒ → SAt → 0
where K∗(At) is the torsion subgroup of …
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.