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Dec 2 at 22:54 comment added Ali Caglayan In dimensions k=1, 2, n-2, n-1, there is a homeomorphism between the realization of the MacPhersonian and the Grassmannian for (k, n) due to MacPherson.
Mar 19, 2013 at 11:28 comment added Marek Krčál At the moment I tend to believe that the Schubert cell decomposition of $BSO(n)$ is not regular (the attaching map can be 2:1 on the codimenison 2 "faces" already, I guess).
Mar 19, 2013 at 11:24 comment added Marek Krčál Thanks for your warning! Another popular-style reference is books.google.com/books?id=mXWr00HurmMC&pg=PA97 that I have read myself! (If I did not find the story boring then and remembered it, I would not get trapped now:))
Mar 19, 2013 at 2:12 comment added S. Carnahan See also arxiv.org/abs/0709.1291
Mar 18, 2013 at 23:21 comment added Matthew Kahle This paper on realizations of MacPhersonians apparently has a fatal flaw, and was later retracted by Biss.
Mar 18, 2013 at 21:48 history answered Marek Krčál CC BY-SA 3.0