Topological Circle Planes and Topological Quadrangles

Introduction, Circle Planes, Introduction, Definitions and Notation, Models for Classical Circle Planes, Derived Structures, Antiregular Quadrangles, Introduction, Generalized Quadrangles, Square Projections, The Twisting Number, Antiregular Quadrangles, Characterization of Antiregular Quadrangles, Laguerre Planes and Antiregular Quadrangles, Introduction , Laguerre Planes Constructed from Antiregular Quadrangles, Antiregular Quadrangles Constructed from Laguerre Planes, Constructing Topologies on the Lie Geometry, Mobius Planes and Antiregular Quadrangles, Introduction , The Lie Geometry of a Mobius Plane, The Lifted Lie Geometry of a Flat Mobius Plane, Constructing Topologies on the Lifted Lie Geometry, Characterizing Quadrangles Obtained from Flat Mobius Planes, Minkowski Planes and Antiregular Quadrangles, Introduction, The Point Space and Parallel Classes, The Circle Space, The Other Spaces, The Derivation of a Minkowski Plane, The Lie Geometry of a Minkowski Plane, The Lifted Lie Geometry of a Minkowski Plane, The Topology on the Lifted Lie Geometry, Characterizing Quadrangles Obtained from Minkowski Planes, Relationship of Circle Planes, Introduction , Sisters of Laguerre Planes, Sisters of Mobius Planes, Sisters of Minkowski Planes, The Problem of Apollonius, Introduction, The Problem of Apollonius in Laguerre Planes, The Problem of Apollonius in Mobius Planes, One Point and Two Circles, Three Circles, The Problem of Apollonius in Minkowski Planes, Two Points and One Circle, One Point and Two circles, Three Circles, Index, Glossary, References