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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 $H^{even}(X; Q)$, …
Efton Park's user avatar
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 …
Efton Park's user avatar
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 …
Efton Park's user avatar
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) …