Cobordisms of immersions with codimension two
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 40-51
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We single out the obstruction for a closed $\mathbb Z_2$-null homologous submanifold of codimension 2 to be the boundary of a submanifold of codimension 1. As an application, we calculate the groups $E\mathscr N_n(\mathbb R^{n+2})$ of cobordisms of embeddings of nonoriented $n$-manifolds in the Euclidean
$n+2$-space for $n=3$ and 4. Namely, we show that $E\mathscr N_3(\mathbb R^2)=\mathbb Z_2$,
$E\mathscr N_4(\mathbb R^6)=0$. A specific generator of the former group is explicitly given.
@article{ZNSL_1998_252_a4,
author = {M. Yu. Zvagel'skii},
title = {Cobordisms of immersions with codimension two},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {40--51},
publisher = {mathdoc},
volume = {252},
year = {1998},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a4/}
}
M. Yu. Zvagel'skii. Cobordisms of immersions with codimension two. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 40-51. http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a4/