An obstruction to the existence of affine structures

DOI10.1007/BF01389273zbMath0485.57015MaRDI QIDQ1164296

John Smillie

Publication date: 1981

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142828

zbMATH Keywords

connected sum of lens spacesfundamental groups of affine manifoldsobstructions to the existence of affine structures and volume preserving affine structures on a compact manifold

Mathematics Subject Classification ID

Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Differential topology (57R99) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (12)

Flat affine or projective geometries on Lie groups ⋮ Universal Lagrangian bundles ⋮ Flat affine manifolds and their transformations ⋮ Classification of Lagrangian fibrations over a Klein bottle ⋮ THE UNIVERSAL COVER OF AN AFFINE THREE-MANIFOLD WITH HOLONOMY OF SHRINKABLE DIMENSION ≤ TWO ⋮ Left-symmetric algebras, or pre-Lie algebras in geometry and physics ⋮ Integrable systems, symmetries, and quantization ⋮ Affine Manifolds and Orbits of Algebraic Groups ⋮ Linear foliations on affine manifolds ⋮ Affine harmonic maps ⋮ The Radiance Obstruction and Parallel Forms on Affine Manifolds ⋮ Non-existence of affine structures on Seifert fibre spaces

Cites Work

• Unnamed Item
• The affine structures on the real two-torus. I
• On the existence of a connection with curvature zero
• Affine manifolds and solvable groups

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