1988 Seminar on Lie Geometry Universidad Central de Venezuela Lectures by Fillmore Pages of notes are displayed at left. The Lie quadric - three figures from course subsequently given at UCSD in 1990 - fig1 fig2 fig3 1988 Seminar 1- 4 : Standing assuptions Main example The hypersphere Homogeneous coördinates 5- 7 : Projective setting Projective space The Lie quadric Oriented sphere or Lie cycle Polars Tangent prime Projective extensions of familiar spaces 8-12 : Stereographic projection Möbius quadric Pole and polar Tangency Oriented contact Parbolic pencil Cones Projection of cones - figure 13 : The Apollonius contact problem 14-17 : Relative power Cross ratio Bunches of Lie cycles 18-24 : Lie contact inversion Appendix - Verification of an identity Remark - row of cycles Some pictures for n = 2 - classical Möbius inversion - Möbius inversion of cycles - Lie contact inversion of cycles - second "envelope" Lie contact inversion - continued - pencil of contact inversions 25-30 : The group of Lie geometry Matrix representation The Lie quadric as homogeneous space The space of contact elements 31-34 : Lie frame Contact densty Special case (Chern) 4 pp : (misc. related to Lie frame) 1-5 : Stiefel manifold - the Möbius quadric - totally isotropic 2-planes - a second sphere - lines - Stiefel manifold - contact form 9 pp : Invariants of Lie geometry Four point invariants General bunch Bunches Types of bunches Case of Euclidean space Search for unruled bunches