Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial
- Innov. Incidence Geom. Algebr. Topol. Comb.
- Volume 17, Number 3 (2019), 221-249.
On two nonbuilding but simply connected compact Tits geometries of type $C_3$
A classification of homogeneous compact Tits geometries of irreducible spherical type, with connected panels and admitting a compact flag-transitive automorphism group acting continuously on the geometry, has been obtained by Kramer and Lytchak (2014; 2019). According to their main result, all such geometries but two are quotients of buildings. The two exceptions are flat geometries of type and arise from polar actions on the Cayley plane over the division algebra of real octonions. The classification obtained by Kramer and Lytchak does not contain the claim that those two exceptional geometries are simply connected, but this holds true, as proved by Schillewaert and Struyve (2017). Their proof is of topological nature and relies on the main result of (Kramer and Lytchak 2014; 2019). In this paper we provide a combinatorial proof of that claim, independent of (Kramer and Lytchak 2014; 2019).
Innov. Incidence Geom. Algebr. Topol. Comb., Volume 17, Number 3 (2019), 221-249.
Received: 27 November 2018
Revised: 12 March 2019
Accepted: 27 April 2019
First available in Project Euclid: 29 October 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Pasini, Antonio. On two nonbuilding but simply connected compact Tits geometries of type $C_3$. Innov. Incidence Geom. Algebr. Topol. Comb. 17 (2019), no. 3, 221--249. doi:10.2140/iig.2019.17.221. https://projecteuclid.org/euclid.iig/1572314476