A Secondary Chern-Euler Class
Copyright policy )A Secondary Chern-Euler Class
Let xi be a smooth oriented vector bundle, with n-dimensional fibre, over a smooth manifold M. Denote by xi-hat the fibrewise one-point compactification of xi. The main purpose of this paper is to define geometrically a canonical element Upsilon(xi) in H^n(xi-hat,Q) (H^n(xi-hat,Z) tensor 1/2, to be more precise). The element ��(��) is a secondary characteristic class to the Euler class in the fashion of Chern-Simons.
8 pages, published version, abstract added in migration
General theory of differentiable manifolds, secondary characteristic class, Poincaré-Hopf index theorem, Geometric Topology (math.GT), Vector fields, frame fields in differential topology, Mathematics - Geometric Topology, index of a vector field, Characteristic classes and numbers in differential topology, FOS: Mathematics, Global differential geometry, Euler class, Thom class
General theory of differentiable manifolds, secondary characteristic class, Poincaré-Hopf index theorem, Geometric Topology (math.GT), Vector fields, frame fields in differential topology, Mathematics - Geometric Topology, index of a vector field, Characteristic classes and numbers in differential topology, FOS: Mathematics, Global differential geometry, Euler class, Thom class
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