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Proceedings of the American Mathematical Society

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Functorial compactification of linear spaces


Author: Chris Kottke
Journal: Proc. Amer. Math. Soc. 147 (2019), 4067-4081
MSC (2010): Primary 54C20, 54D30, 58A05
DOI: https://doi.org/10.1090/proc/14452
Published electronically: June 14, 2019
MathSciNet review: 3993798
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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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Additional Information

Chris Kottke
Affiliation: Department of Mathematics, New College of Florida, 5800 Bay Shore Road, Sarasota, Florida 34243
Email: ckottke@ncf.edu

DOI: https://doi.org/10.1090/proc/14452
Received by editor(s): June 14, 2018
Published electronically: June 14, 2019
Communicated by: Guofang Wei
Article copyright: © Copyright 2019 American Mathematical Society