FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 1, PAGES 173-197

**Spaces of immersions of elementary fibre bundles**

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 $Dk$´
D^{l} ® D^{k}, we give
a definition of fibrewise immersion and for fibre boundary
spheres (fibre bundles $$¶D^{k} ´ D^{l} ® ¶D^{k},
$Dk$´ ¶D^{l} ® D^{k} and
$$¶D^{k} ´ ¶D^{l} ® ¶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