Abstract:
The surgery obstruction groups for a manifold pair were introduced by
Wall for the study of the surgery problem on a manifold with a submanifold. These groups are closely related to the problem of splitting a homotopy equivalence along a submanifold and have been used in many geometric and topological applications.
In the present paper the concept of surgery on a triple of manifolds
is introduced and algebraic and geometric properties of the corresponding
obstruction groups are described. It is then shown that these groups are closely related to the normal invariants and the classical splitting and surgery obstruction groups, respectively,
of the manifold in question. In the particular case of one-sided submanifolds relations between the newly introduced groups and the surgery spectral sequence constructed by
Hambleton and Kharshiladze are obtained.
\Bibitem{MurRepSpa03}
\by Yu.~V.~Muranov, D.~Repov{\v s}, F.~Spaggiari
\paper Surgery on triples of manifolds
\jour Sb. Math.
\yr 2003
\vol 194
\issue 8
\pages 1251--1271
\mathnet{http://mi.mathnet.ru/eng/sm764}
\crossref{https://doi.org/10.1070/SM2003v194n08ABEH000764}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2034535}
\zmath{https://zbmath.org/?q=an:1067.57032}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000186261600016}
\elib{https://elibrary.ru/item.asp?id=14327467}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0344629363}
Linking options:
https://www.mathnet.ru/eng/sm764
https://doi.org/10.1070/SM2003v194n08ABEH000764
https://www.mathnet.ru/eng/sm/v194/i8/p139
This publication is cited in the following 9 articles:
A. Cavicchioli, Yu. V. Muranov, F. Spaggiari, F. Hegenbarth, “On Iterated Browder–Livesay Invariants”, Math. Notes, 86:2 (2009), 196–215
Cavicchioli A., Muranov Yu.V., Spaggiari F., “Assembly maps and realization of splitting obstructions”, Monatsh. Math., 158:4 (2009), 367–391
Cavicchioli A., Muranov Yu.V., Spaggiari F., “Surgery on pairs of closed manifolds”, Czechoslovak Math. J., 59:2 (2009), 551–571
Jimenez R., Muranov Yu.V., Repovš D., “Splitting along a submanifold pair”, J. K-Theory, 2:2, Special issue in memory of Yurii Petrovich Solovyev, Part 1 (2008), 385–404
A. Bak, Yu. V. Muranov, “Splitting a simple homotopy equivalence along a submanifold with filtration”, Sb. Math., 199:6 (2008), 787–809
Yu. V. Muranov, D. Repovš, M. Cencelj, “The $\pi$-$\pi$-Theorem for Manifold Pairs”, Math. Notes, 81:3 (2007), 356–364
Yu. V. Muranov, R. Himenez, “Transfer maps for triples of manifolds”, Math. Notes, 79:3 (2006), 387–398
Cavicchioli A., Muranov Yu.V., Spaggiari F., “Mixed structures on a manifold with boundary”, Glasg. Math. J., 48:1 (2006), 125–143
Yu. V. Muranov, R. Jimenez, “Structure sets of triples of manifolds”, J. Math. Sci., 144:5 (2007), 4468–4483
Citation in format AMSBIB
Contact us: