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Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
16
votes
1
answer
2k
views
What is an example of a compact smooth manifold whose K-theory and Cech cohomology are not i...
On page 283 of Max Karoubi’s book, “K-theory,” he states that for any compact Hausdorff space $X$, the Chern character determines an isomorphism from the group $K^0(X) \otimes Q$ to $H^{even}(X; Q)$, …
1
vote
Relative K-theory and split exact sequences of C* algebras
For the case where $A = C(X)$ for some compact Hausdorff space and $J$ is an ideal in $A$, the lemma you state is Theorem 2.2.10 in my book "Complex Topological K-Theory." As the title suggests, I on …
2
votes
1
answer
432
views
Map from algebraic K-theory to topological K-theory
Suppose that $A$ is a Banach algebra with unit. We can consider $GL(A)$ as a topological group in either the discrete topology or the topology that it inherits from the norm topology of $A$, and the …
25
votes
Textbook or lecture notes in topological K-Theory
I wrote a book that may be what you are looking for. It's called "Complex Topological K-Theory," and it is published by Cambridge University Press. As the title suggests, I do not discuss real (KO) …