Abstract
The flag-homogeneous compact connected polygons with equal topological parametersp = q are classified explicitly. These polygons turn out to be Moufang polygons.
Similar content being viewed by others
References
Adams, J. F. and Atiyah, M. F.:K-theory and the Hopf invariant,Quart. J. Math. Oxford (2) 17 (1966), 31–38.
Arens, R.: Topologies for homeomorphism groups,Amer. J. Math. 68 (1946), 593–610.
Ball, B.J.: Arcwise connectedness and the persistence of errors,Amer. Math. Monthly 91 (1984), 431–433.
Bickel, H.: Lie-projektive Gruppen: Vergeleich von Approximationsbegriffen, Diplomarbeit Braunschweig, 1992.
Borel, A.: La cohomologie mod 2 de certains espaces homogénes,Comment. Math. Helv. 27 (1953), 165–197.
Borel, A. and De Siebenthal, J.: Les sous-groupes fermés de rang maximum des groupes de Lie clos,Comment. Math. Helv. 23 (1949), 200–221.
Brouwer, A. E.: A non-degenerate generalized quadrangle with lines of size four is finite, in J. W. P. Hirschfeldet al. (eds)Proc. Brighton 1990, Oxford University Press 1991, pp. 47–49.
Burns, K. and Spatzier, R.: On topological Tits buildings and their classification,Publ. Math. I.H.E.S. 65 (1987), 5–34.
Dienst, K. J.: Verallgemeinerte Vierecke in projektiven Räumen,Arch. Math. 35 (1980), 177–186.
Dugundji, J.:Topology, Allyn and Bacon, Boston, 1966.
Engelking, R.:General Topology, Heldermann Verlag, Berlin, 1989.
Engelking, R. and Sieklucki, K.:Topology. A Geometric Approach, Heldermann Verlag, Berlin, 1992.
Feit, W.: Finite projective planes and a question about primes,Proc. Amer. Math. Soc. 108 (1990), 561–564.
Ferus, D., Karcher, H. and Münzner, H.-F.: Cliffordalgebren und neue isoparametrische Hyperflächen,Math. Z. 177 (1981), 479–502.
Fink, J. B.: Flag-transitive projective planes,Geom. Dedicata 17 (1985), 219–226.
Freudenthal, H.: Einige Sätze über topologische Gruppen,Ann. Math. 37 (1936), 44–56.
Gluškov, V. M.: The structure of locally compact groups and Hilbert's fifth problem,Amer. Math. Soc. Transl. (2),15 (1960), 55–93.
Grove, K. and Halperin, S.: Dupin hypersurfaces, group actions, and the double mapping cylinder,J. Differential Geom. 26 (1987), 429–459.
Grundhöfer, T.: Ternary fields of compact projective planes,Abh. Math. Sem. Univ. Hamburg 57 (1986), 87–101.
Grundhöfer, T.: Automorphism groups of compact projective planes,Geom. Dedicata 21 (1986), 291–298.
Grundhöfer, T. and Knarr, N.: Topology in generalized quadrangles,Topology Appl. 34 (1990), 139–152.
Grundhöfer, T. and Van Maldeghem, H.: Topological polygons and affine buildings of rank three,Atti Sem. Mat. Fis. Univ. Modena 38 (1990), 459–479.
Hähl, H.: Automorphismengruppen achtdimensionaler lokalkompakter Quasikörper,Math. Z. 149 (1976), 203–225.
Hebda, J. J.: The possible cohomology rings of certain types of taut submanifolds,Nagoya Math. J. 111 (1988), 85–97.
Helgason, S.:Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, San Diego, 1978.
Hsiang, W.-Y. and Lawson, H. B.: Minimal submanifolds of low cohomogeneity,J. Differential Geom. 5 (1971), 1–38.
Hothi, A.: Another alternative proof of Effros' Theorem,Topology Proc. 12 (1987), 256–298.
Kantor, W. M.: Flag-transitive planes, in C. A. Baker and L. M. Batten (eds.),Finite Geometries, Proc. Winnipeg 1984, Dekker, New York, 1985, pp. 179–181.
Kantor, W. M.: Primitive permutation groups of odd degree, and an application to finite projective planes,J. Algebra 106 (1987), 15–45.
Knarr, N.: Projectivities of generalized polygons,Ars Combin. 25B (1988), 265–275.
Knarr, N.: The nonexistence of certain topological polygons,Forum Math. 2 (1990), 603–612.
Kramer, L.: Gebäude auf isoparametrischen Untermannigfaltigkeiten, Diplomarbeit Tübingen, 1991.
Kuratowski, K.:Topology, Vol. II, Academic Press, New York, 1968.
Löwen, R.: Homogeneous compact projective planes,J. reine angew. Math. 321 (1981), 217–220.
Lunardon, G. and Pasini, A.: FiniteC n geometries: a survey,Note di Matematica 10 (1990), 1–35.
Montgomery, D.: Simply connected homogeneous spaces,Proc. Amer. Math. Soc. 1 (1950), 467–469.
Montgomery, D. and Zippin, L.:Topological Transformation Groups, Interscience Publishers, New York, 1955.
Münzner, H.-F.: Isoparametrische Hyperflächen in Sphären II,Math. Ann. 256 (1981), 215–232.
Ronan, M.:Lectures on Buildings, Academic Press, San Diego, 1989.
Salzmann, H.: Topologische projektive Ebenen,Math. Z. 67 (1957), 436–466.
Salzmann, H.: Kompakte zweidimensionale projektive Ebenen,Math. Ann. 145 (1962), 401–428.
Schurle, A. W.:Topics in Topology, Elsevier North Holland, New York, 1979.
Szenthe, J.: On the topological characterization of transitive Lie group actions,Acta Sci. Math. (Szeged) 36 (1974), 323–344.
Takagi, R. and Takahashi, T.: On the principal curvatures of homogeneous hypersurfaces in a sphere, in S. Kobayashi, M. Obata and T. Takahashi (eds),Differential Geometry, in honor of Kentaro Yano, Kinokuniya, Tokyo, 1972, pp. 469–481.
Thorbergsson, G.: Clifford algebras and polar planes,Duke Math. J. 67 (1992), 627–632.
Tits, J.: Sur la trialité et certaines groupes qui s'en déduisent,Publ. Math. I.H.E.S. 2 (1959), 14–60.
Tits, J.:Buildings of Spherical Type and Finite BN-Pairs (2nd edn), Lecture Notes in Maths 386, Springer, Berlin, 1986.
Wang, H.-C.: Homogeneous spaces with non-vanishing Euler characteristics,Ann. Math. (2) 50 (1949), 469–481.
Wang, Q.-M.: On the topology of Clifford isoparametric hypersurfaces,J. Diff. Geom. 27 (1988), 55–66.
Warner, G.:Harmonic Analysis on Semi-simple Lie Groups, Springer, 1972.
Wolf, J. A.:Spaces of Constant Curvature, Publish or Perish, Wilmington, 1984.