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
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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.
@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
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/