FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 1, PAGES 173-197
S. M. Tuleshev
Abstract
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In the paper we consider immersions of elementary fibre objects. For fibre
disk, i. e.\ a trivial fibre bundle of type $D^k\times D^l \to D^k$ , we give
a definition of fibrewise immersion and for fibre boundary spheres (fibre
bundles $\partial D^k\times D^l \to \partial D^k$ ,
$D^k\times \partial D^l \to D^k$
and $\partial D^k\times \partial D^l \to \partial D^k$ )
we define the notion of framed
fibrewise immersions. It is proved that the natural maps from the space of
immersions of fibre disk into spaces of framed immersions of fibre boundary
spheres satisfy the axiom of the covering homotopy, i. e.\ are Serre bundles.
This result is an initial step in solving the problem on the homotopy
description of space of immersions of one fibre manifold into another fibre
manifold.
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Last modified: May 10, 2001