Sbornik. Mathematics, Tome 14 (1971) no. 3, pp. 359-366
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A. S. Mishchenko. Surgery of Poincaré complexes. Sbornik. Mathematics, Tome 14 (1971) no. 3, pp. 359-366. http://geodesic.mathdoc.fr/item/SM_1971_14_3_a2/
@article{SM_1971_14_3_a2,
author = {A. S. Mishchenko},
title = {Surgery of {Poincar\'e} complexes},
journal = {Sbornik. Mathematics},
pages = {359--366},
year = {1971},
volume = {14},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1971_14_3_a2/}
}
TY - JOUR
AU - A. S. Mishchenko
TI - Surgery of Poincaré complexes
JO - Sbornik. Mathematics
PY - 1971
SP - 359
EP - 366
VL - 14
IS - 3
UR - http://geodesic.mathdoc.fr/item/SM_1971_14_3_a2/
LA - en
ID - SM_1971_14_3_a2
ER -
%0 Journal Article
%A A. S. Mishchenko
%T Surgery of Poincaré complexes
%J Sbornik. Mathematics
%D 1971
%P 359-366
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1971_14_3_a2/
%G en
%F SM_1971_14_3_a2
In the paper one studies the problem of extending the method of Morse surgery for the study of smooth manifolds to the case of the category of Poincaré complexes. In the latter case we compute an obstruction to the surgery of a Poincaré complex up to homotopy equivalence which, as in the classical case, is in the Wall group. In contrast to the cases of smooth or combinatorial manifolds we are able to handle only complexes with vanishing boundary. Bibliography: 3 titles.
