@article{SM_1970_12_1_a4,
author = {V. R. Kireitov},
title = {On~symplectic cobordisms},
journal = {Sbornik. Mathematics},
pages = {77--89},
year = {1970},
volume = {12},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1970_12_1_a4/}
}
TY - JOUR
AU - V. R. Kireitov
TI - On symplectic cobordisms
JO - Sbornik. Mathematics
PY - 1970
SP - 77
EP - 89
VL - 12
IS - 1
UR - http://geodesic.mathdoc.fr/item/SM_1970_12_1_a4/
LA - en
ID - SM_1970_12_1_a4
ER -
%0 Journal Article
%A V. R. Kireitov
%T On symplectic cobordisms
%J Sbornik. Mathematics
%D 1970
%P 77-89
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1970_12_1_a4/
%G en
%F SM_1970_12_1_a4
In the article, the method of spherical reconstructions of smooth manifolds is applied to the computation of some groups of symplectic cobordisms. Namely, it is proved that $\Omega^5_{Sp}=Z_2$, $\Omega^6_{Sp}=Z_2$, $\Omega^7_{Sp}=0$. The indicated values of the groups of cobordisms for dimensions 5 and 6 are known and follow from arguments of the Adams spectral sequence for $S_p$-cobordisms. The new result is the fact that the seventh group of cobordisms equals 0. This is the fundamental result of the article. The theorem concerning the reconstruction of manifolds with a quasisymplectic structure in the normal bundle, which is proved in the article, and the theorem on integer values of Atiyah–Hirzebruch constitute the basis for the proof. Bibliography: 6 titles.
