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I'm currently reading Michor, Manifold of Mappings for Continuum Mechanics. In this paper he makes use of 'Whitney Jets' but takes it to be an already understood concept. I'm familiar with jets but have not come across Whitney jets in my reading. Googling the term didn't help as it brought up a slew of papers who also assumed the notion as known.

Q. What is a Whitney jet, how does it differ from an ordinary jet and what is it useful for. Also a recent reference for the definition would be useful.

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    $\begingroup$ On page 12 of the article you mentioned Michor defines Whitney jets (look for the paragraph that starts "More details:".) $\endgroup$
    – Willie Wong
    Commented Jun 12 at 22:48
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    $\begingroup$ Basically a finite order Whitney jet is the geometric version of the sort of data you will need to prescribe for Whitney's extension theorem, and you take a suitable limit to get to the infinite order version. Note that in the extension theorem, the underlying set may fail to have a manifold structure, and so one cannot use the jet bundle formalism. One purpose of Whitney jets is to get around this. Michor seems to be using this idea to study mappings whose domain are more singular than standard manifolds. $\endgroup$
    – Willie Wong
    Commented Jun 12 at 22:53
  • $\begingroup$ Since Michor is on mathOverflow, maybe he will drop by and give an authoritative answer. $\endgroup$
    – Willie Wong
    Commented Jun 12 at 22:55
  • $\begingroup$ @Willie Wong: Thxs for pointing that out, I missed that. I expected the definition to appear before its use ;-). If you post your comment as an answer I can accept it. $\endgroup$
    – Mozibur Ullah
    Commented Jun 13 at 1:28

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converted from comments:

On page 12 or the article mentioned, the author defines Whitney jets (look for the paragraph that starts with "More details.")

But basically, the classical jet bundle is only really defined for mappings between manifolds. In the article Michor is trying to treat mappings whose domain may be more singular. What he means by Whitney jets are similar (in the finite order case) to what is prescribed as the data for Whitney's extension theorem.

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  • $\begingroup$ Thanks again for the answer! $\endgroup$
    – Mozibur Ullah
    Commented Jun 30 at 6:16

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