دانلود کتاب Compact Projective Planes: With an Introduction to Octonion Geometry

فهرست مطالب :

Preface\nChapter 1. The classical planes\n11 The classical division algebras\n12 The classical affine planes\n13 The projective planes over ℝ, ℂ, and ℍ\n14 The planes over ℝ, ℂ, and ℍ as topological planes\n15 Geometry of a projective line\n16 The projective octonion plane P2O\n17 The collineation group of P2O\n18 Motion groups of P2O\nChapter 2. Background on planes, coordinates and collineations\n21 Projective and affine planes\n22 Coordinates, ternary fields\n23 Collineations\n24 Lenz-Barlotti types\n25 Translation planes and quasifields\nChapter 3. Geometries on surfaces\n31 ℝ2-planes\n32 Two-dimensional compact projective planes\n33 Towards classification\n34 The Moulton planes\n35 Skew hyperbolic planes\n36 Skew parabola planes\n37 Planes over Cartesian fields\n38 Flexibility, rigidity and related topics\nChapter 4. Compact projective planes\n41 The topology of locally compact planes\n42 Compact, connected planes\n43 Ternary fields for compact planes\n44 Automorphism groups\nChapter 5. Algebraic topology of compact, connected planes\n51 General properties\n52 Assuming that lines are manifolds\n53 Conditions implying that lines are manifolds\n54 Lines are homology manifolds\n55 Geometric consequences\nChapter 6. Homogeneity\n61 Axial collineations\n62 Planes admitting a classical motion group\n63 Transitive groups\n64 Transitive axial groups\n65 Groups of large dimension\n66 Remarks on von Staudt’s point of view\nChapter 7. Four-dimensional planes\n71 Automorphism groups\n72 Characterizing P2ℂ\n73 Four-dimensional translation planes\n74 Four-dimensional shift planes\n75 Analytic planes\nChapter 8. Eight- and sixteen-dimensional planes\n81 Translation planes\n82 Classification of translation planes\n83 Stiffness\n84 Characterizing\n85 Characterizing P2O\n86 Hughes planes\n87 Principles of classification\nChapter 9. Appendix: Tools from topology and Lie theory\n91 Permutation groups\n92 Topological dimension and remarks on general topology\n93 Locally compact groups and Lie groups\n94 Lie groups and their structure\n95 Linear representations\n96 Transformation groups\nBibliography\nNotation\nIndex