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arXiv · 1006.4352

The space of ideals of C^\infty(M,R)

Lukáš Vokřínek
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Abstract

The paper is concerned with defining a topology on the set of ideals of codimension d of the algebra C^\infty(M,R) with M being a compact smooth manifold. Its main property is that it is compact Hausdorff and it contains as a subspace the configuration space of d distinct unordered points in M and therefore provides a "compactification" of this configuration space. It naturally forms a space over the symmetric product SP_d(M) and as such has a very rich structure. Moreover it is covered by a (naturally defined) set of charts in which it is semialgebraic.

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BibTeXRIS

Lukáš Vokřínek. 2010-06-22. The space of ideals of C^\infty(M,R). https://arxiv.org/abs/1006.4352

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