Surgery on pairs of closed manifolds

Alberto Cavicchioli; Yuri V. Muranov; Fulvia Spaggiari

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 2, page 551-571
  • ISSN: 0011-4642

Abstract

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To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group L P * generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the case of an elementary fundamental group. Then we generalize them, and obtain several further results about the realization of elements in the Browder-Quinn surgery obstruction groups by means of normal maps to a closed manifold filtered by closed submanifolds.

How to cite

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Cavicchioli, Alberto, Muranov, Yuri V., and Spaggiari, Fulvia. "Surgery on pairs of closed manifolds." Czechoslovak Mathematical Journal 59.2 (2009): 551-571. <http://eudml.org/doc/37940>.

@article{Cavicchioli2009,
abstract = {To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group $LP_*$ generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the case of an elementary fundamental group. Then we generalize them, and obtain several further results about the realization of elements in the Browder-Quinn surgery obstruction groups by means of normal maps to a closed manifold filtered by closed submanifolds.},
author = {Cavicchioli, Alberto, Muranov, Yuri V., Spaggiari, Fulvia},
journal = {Czechoslovak Mathematical Journal},
keywords = {surgery on manifolds; surgery obstruction groups for a manifold pair; assembly map; splitting problem; Browder-Livesay groups; Browder-Quinn surgery obstruction groups; splitting obstruction groups; manifolds with filtration; surgery on manifolds; surgery obstruction groups for a manifold pair; assembly map; splitting problem; Browder-Livesay group; Browder-Quinn surgery obstruction group; splitting obstruction group; manifold with filtration},
language = {eng},
number = {2},
pages = {551-571},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Surgery on pairs of closed manifolds},
url = {http://eudml.org/doc/37940},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Cavicchioli, Alberto
AU - Muranov, Yuri V.
AU - Spaggiari, Fulvia
TI - Surgery on pairs of closed manifolds
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 551
EP - 571
AB - To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group $LP_*$ generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the case of an elementary fundamental group. Then we generalize them, and obtain several further results about the realization of elements in the Browder-Quinn surgery obstruction groups by means of normal maps to a closed manifold filtered by closed submanifolds.
LA - eng
KW - surgery on manifolds; surgery obstruction groups for a manifold pair; assembly map; splitting problem; Browder-Livesay groups; Browder-Quinn surgery obstruction groups; splitting obstruction groups; manifolds with filtration; surgery on manifolds; surgery obstruction groups for a manifold pair; assembly map; splitting problem; Browder-Livesay group; Browder-Quinn surgery obstruction group; splitting obstruction group; manifold with filtration
UR - http://eudml.org/doc/37940
ER -

References

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