Functorial compactification of linear spaces

Kottke, Chris

doi:10.1090/proc/14452

Functorial compactification of linear spaces
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Proc. Amer. Math. Soc. 147 (2019), 4067-4081 Request permission

Abstract:

We define compactifications of vector spaces which are functorial with respect to certain linear maps. These “many-body” compactifications are manifolds with corners, and the linear maps lift to b-maps in the sense of Melrose. We derive a simple criterion under which the lifted maps are in fact b-fibrations, and identify how these restrict to boundary hypersurfaces. This theory is an application of a general result on the iterated blow-up of cleanly intersecting submanifolds which extends related results in the literature.

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