Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 1, pp. 66-90
Citer cet article
E. A. Polulyakh. On embedding of total spaces of fiber bundles over a circle with the Cantor set as a fiber in two-dimensional manifolds. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 1, pp. 66-90. http://geodesic.mathdoc.fr/item/JMAG_2000_7_1_a3/
@article{JMAG_2000_7_1_a3,
author = {E. A. Polulyakh},
title = {On embedding of total spaces of fiber bundles over a~circle with the {Cantor} set as a fiber in two-dimensional manifolds},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {66--90},
year = {2000},
volume = {7},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/JMAG_2000_7_1_a3/}
}
TY - JOUR
AU - E. A. Polulyakh
TI - On embedding of total spaces of fiber bundles over a circle with the Cantor set as a fiber in two-dimensional manifolds
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 2000
SP - 66
EP - 90
VL - 7
IS - 1
UR - http://geodesic.mathdoc.fr/item/JMAG_2000_7_1_a3/
LA - ru
ID - JMAG_2000_7_1_a3
ER -
%0 Journal Article
%A E. A. Polulyakh
%T On embedding of total spaces of fiber bundles over a circle with the Cantor set as a fiber in two-dimensional manifolds
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2000
%P 66-90
%V 7
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2000_7_1_a3/
%G ru
%F JMAG_2000_7_1_a3
The problem of an embedding of total spaces of fiber bundles over a circle with the Cantor set as a fiber (Pontryagin bundles) in two-dimensional manifolds is investigated. The sufficient condition is obtained for nonexistence of a two-dimensional manifold $M^{2}$ and inclusion map $\Phi\colon N\to M^2$ for total space $N$ of the Pontryagin bundle $\xi=(N,p,S^1)$. We also construct the extensive class of spaces satisfying the condition.
