I would like to learn the theorem which states that K-theory defined in terms of vector bundles is isomorphic to the so called compactly supported complexes (those are complexes of vector bundles over locally compact space $X$ of the form $0 \to E_1 \to E_2 \to ... \to E_n \to 0$ where this sequence is exact except for some compact set $A \subset X$). I would be happy with the proof from which it is clear how the maps establishing isomorphism look like. I would be grateful for pointing me some references.
K-theory as elliptic complexes
2
$\begingroup$
reference-request
vector-bundles
k-theory
-
1I'm not sure if this is exactly what you want, but you should check out definition 9.23, and propositions 9.24, 9.25 in chapter I of Lawson and Michelsohn's *Spin Geometry*. – 2017-02-06
-
0I strongly recommend Atiyah-Bott-Shapiro's Clifford Modules, Part II, for a start. – 2017-02-06