nLab
jet space

Idea

The notion of jet space or jet bundle is a generalization of the notion of tangent spaces and tangent bundles, respectively. While a tangent vector is an equivalence class of germs of curves with order-$1$ tangency at a given point in the target, jet spaces are equivalence classes of germs of smooth maps with respect to (finite) order-$k$ tangency at some point in the target.

References

Jet bundles were first introduced by Charles Ehresmann.

• wikipedia: jet, jet bundle

• Ivan Kolar, Jan Slovak, Peter W. Michor, Natural operations in differential geometry, book 1993, 1999, pdf, hyper-dvi, ps

• G. Sardanashvily, Fibre bundles, jet manifolds and Lagrangian theory, Lectures for theoreticians, arXiv:0908.1886

• Shihoko Ishii, Jet schemes, arc spaces and the Nash problem, arXiv:math.AG/0704.3327

• D. J. Saunders, The geometry of jet bundles, London Mathematical Society Lecture Note Series 142, Cambridge Univ. Press 1989.