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- W3045899313 abstract "The Whitney group $K_1(A)$ is isomorphic to $A^times times operatorname{SK}_1(A)$ for some subgroup $operatorname{SK}_1(A)$, where $A$ is a commutative ring and $A^times$ denotes the set of units in $A$. Consider an o-minimal expansion of a real closed field $mathcal R=(R,0,1,+,cdot,ldots)$. Let $M$ be an affine definable $C^r$ manifold, where $r$ is a nonnegative integer. We demonstrate its homotopy theorem and that the group $operatorname{SK}_1(C_{text{df}}^r)$ is isomorphic to $operatorname{SK}_1(C_{text{df}}^0(M))$, where $C_{text{df}}^r(M)$ denotes the ring of definable $C^r$ functions on $M$." @default.
- W3045899313 created "2020-08-03" @default.
- W3045899313 creator A5064823367 @default.
- W3045899313 date "2020-07-29" @default.
- W3045899313 modified "2023-09-27" @default.
- W3045899313 title "Whitehead group of the ring of smooth functions definable in an o-minimal structure" @default.
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