Subject: Re: 3 postings
Date: Mon, 18 Mar 2002 19:07:17 -0500 (EST)
From: Yuli Rudyak <rudyak@math.ufl.edu>
To: dmd1@lehigh.edu

> Subject: question about char. classes
> Date: Wed, 13 Mar 2002 15:23:16 +0400 (IRT)
> From: rezazadegan@math.sharif.edu
>
> There is a sentense in
>
> "M. Atyiah Collected works, vol 3  ,p77"
>
> about charecteristic classes wich says:
>
> "Roughly speaking one considers the cycles where a given number of
> vector
> fields becomes linearly dependent."
>
> What is the meaning of this sentence?
>

This was the original definition of Pontryagin characteristic classes, given by
Pontryagin. He considered fields of $k$-frames on a manifold and looked for sets
(homology classes) where the rank decreases. See the review

9,243f 56.0X
Pontryagin, L. S.
Characteristic cycles on differentiable manifolds. (Russian)
Mat. Sbornik N. S. 21(63), (1947). 233--284.

Dr. Yuli B. Rudyak
Department of Mathematics
University of Florida
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