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- Title
AFFINE CONNECTIONS AND SECOND-ORDER AFFINE STRUCTURES: Dedicated to my good friend Tom Rewwer on the occasion of his 35th birthday.
- Authors
BÁR, Filip
- Abstract
Smooth manifolds have been always understood intuitively as spaces with an affine geometry on the infinitesimal scale. We make this notion precise within Synthetic Differential Geometry by showing that every manifold carries a natural structure of an infinitesimally affine space, which we interpret as the action of the clone of affine combinations on a first-order infinitesimal structure constructed from the first neighbourhood of the diagonal. We define a second-order infinitesimal structure based on the second neighbourhood of the diagonal and show that on any manifold a symmetric affine connection extends to a second-order infinitesimally affine structure using the log-exp bijection induced by the connection.
- Subjects
AFFINE geometry; ALGEBRAIC equations; SYMMETRIC functions; BLOWING up (Algebraic geometry); FUNCTOR theory
- Publication
Cahiers de Topologie et Geometrie Differentielle Categoriques, 2022, Vol 63, Issue 1, p35
- ISSN
1245-530X
- Publication type
Article