The K-group of R-constructible Sheaves

Details The K-group of R-constructible Sheaves The K-group of R-constructible Sheaves

2002-09-04

arxiv.org/abs/math/0209034v8

Mathematics

Differential Geometry

4 pages, no figures, LaTeX

Scientific paper

Let Z be a smooth projective manifold. In these notes I will prove that the K-group of R-constructible sheaves is isomorphic to the free abelian group with one generator for each open semialgebraic subset $U$ (which I will denote by the same letter) modulo the Mayer-Vietoris relations: U + V - U^V - UvV = 0. I will prove it by showing that both groups in question are isomorphic to the group of all integer-valued semialgebraic functions on Z.

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