2018/01/16 by Anneleen De Schepper, N. S. Narasimha Sastry, Hendrik Van Maldeghem
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Class (philosophy) #Homotopy and Cohomology in Algebraic Topology #Point (geometry) #Polarity (international relations) #Symplectic geometry #Symplectomorphism #Type (biology) #math.CO #msc:51E24
paper · pdf · doi:10.1007/s12188-017-0190-5
published as Abh. Math. Semin. Univ. Hambg. (2018) 88:97--160 · 64 pages
crossref issued 2018/01/16 · crossref published 2018/01/16 · crossref published-online 2018/01/16 · openalex publication_date 2018/01/16 · crossref created 2018/01/16 · openalex created_date 2018/01/26 · crossref published-print 2018/04/01 · crossref deposited 2019/01/16 · arxiv created 2020/01/10 · arxiv updated 2020/01/13 · crossref indexed 2026/08/01 · openalex updated_date 2026/08/05
A symplectic polarity of a building Δ of type E6 is a polarity whose fixed point structure is a building of type F4 containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type F4). In this paper, we show in a geometric way that every building of type E6 contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type F4 fully embedded in the natural point-line geometry of Δ arises from a symplectic polarity.