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arXiv 2004.00097math.MGmath.DGmath.RT
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轨道空间的提升等距

Lifting isometries of orbit spaces

Ricardo A. E. Mendes

备注：
9 pages. Final version, to appear in the Bulletin of the London Mathematical Society. Compared to the previous version, one of the corollaries to the main result has been reformulated as an easy-to-use formula (Proposition 5(b)). Moreover, many improvements to the presentation have been made, including the addition of a new section (Section 2)
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摘要：

给出紧致群的一个正交表示，证明了轨道空间的等距群的连通分支的任何元素提升到原欧几里得空间的等变等距。推论包括这个连通分量的一个简单公式，它适用于“大多数”表示。

英文摘要：

Given an orthogonal representation of a compact group, we show that any element of the connected component of the isometry group of the orbit space lifts to an equivariant isometry of the original Euclidean space. Corollaries include a simple formula for this connected component, which applies to ``most'' representations.

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