@article{0440f9eee1bb43eeb86e6cabed070576,
title = "Determinantal variety and normal embedding",
abstract = "The space GLn+ of matrices of positive determinant inherits an extrinsic metric space structure from {\^a}n2. On the other hand, taking the infimum of the lengths of all paths connecting a pair of points in GLn+ gives an intrinsic metric. We prove bi-Lipschitz equivalence between intrinsic and extrinsic metrics on GLn+, exploiting the conical structure of the stratification of the space of n × n matrices by rank.",
keywords = "Determinantal variety, bi-Lipschitz equivalence, conical stratification, intrinsic metric",
author = "K. Katz and M. Katz and D. Kerner and Y. Liokumovich",
note = "Funding Information: M.K. was partially funded by the Israel Science Foundation grant No. 1517/12. D.K. was partially supported by the Israel Science Foundation grant 844/14. This paper answers a question posed by Asaf Shachar at MOa and we thank him for posing the question. We are grateful to Yves Cornulier for a helpful comment posted there. We are grateful to Jake Solomon for providing the proof in Sec. 4 of the general case of the bi-Lipschitz property for the determinantal variety. We thank Jason Starr for a helpful comment posted at MO.b We thank Amitai Yuval for pointing out a gap in an earlier version of the article, and Alik Nabutovsky and Kobi Peterzil for useful suggestions. Publisher Copyright: {\textcopyright} 2018 World Scientific Publishing Company.",
year = "2018",
month = mar,
day = "1",
doi = "10.1142/S1793525318500073",
language = "English",
volume = "10",
pages = "27--34",
journal = "Journal of Topology and Analysis",
issn = "1793-5253",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "1",
}