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List of contents
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, Möbius Planes and Antiregular Quadrangles, Introduction , The Lie Geometry of a Möbius Plane, The Lifted Lie Geometry of a Flat Möbius Plane, Constructing Topologies on the Lifted Lie Geometry, Characterizing Quadrangles Obtained from Flat Möbius 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 Möbius Planes, Sisters of Minkowski Planes, The Problem of Apollonius, Introduction, The Problem of Apollonius in Laguerre Planes, The Problem of Apollonius in Möbius 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
About the author
Andreas E Schroth
Summary
This research note presents a complete treatment of the connection between topological circle planes and topological generalized quadrangles
