On algebraic K-theory of real algebraic varieties with circle action

✍ Scribed by Yildiray Ozan

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 89 KB
• Volume: 170
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(01)00129-3

✦ Synopsis

Assume that X is a compact connected orientable nonsingular real algebraic variety with an algebraic free S 1 -action so that the quotient Y = X=S 1 is also a real algebraic variety. If : X → Y is the quotient map then the induced map between reduced algebraic K-groups,

X ) denoting the ring of entire rational (regular) functions on the real algebraic variety X , extending partially the Bochnak-Kucharz result that K0(R(X × S 1 ; C)) = K0(R(X; C)) for any real algebraic variety X . As an application we will show that for a compact connected Lie group G K0(R(G; C)) ⊗ Q = 0.