Geodesic
Groups of obstructions to surgery and splitting for a manifold pair
Sbornik. Mathematics, Tome 188 (1997) no. 3, pp. 449-463 
Yu. V. Muranov; D. Repovš. Groups of obstructions to surgery and splitting for a manifold pair. Sbornik. Mathematics, Tome 188 (1997) no. 3, pp. 449-463. http://geodesic.mathdoc.fr/item/SM_1997_188_3_a5/
@article{SM_1997_188_3_a5,
     author = {Yu. V. Muranov and D. Repov\v{s}},
     title = {Groups of obstructions to surgery and splitting for a~manifold pair},
     journal = {Sbornik. Mathematics},
     pages = {449--463},
     year = {1997},
     volume = {188},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_3_a5/}
}
TY  - JOUR
AU  - Yu. V. Muranov
AU  - D. Repovš
TI  - Groups of obstructions to surgery and splitting for a manifold pair
JO  - Sbornik. Mathematics
PY  - 1997
SP  - 449
EP  - 463
VL  - 188
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1997_188_3_a5/
LA  - en
ID  - SM_1997_188_3_a5
ER  - 
%0 Journal Article
%A Yu. V. Muranov
%A D. Repovš
%T Groups of obstructions to surgery and splitting for a manifold pair
%J Sbornik. Mathematics
%D 1997
%P 449-463
%V 188
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1997_188_3_a5/
%G en
%F SM_1997_188_3_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

The surgery obstruction groups $LP_*$ of manifold pairs are studied. An algebraic version of these groups for squares of antistructures of a special form equipped with decorations is considered. The squares of antistructures in question are natural generalizations of squares of fundamental groups that occur in the splitting problem for a one-sided submanifold of codimension 1 in the case when the fundamental group of the submanifold is mapped epimorphically onto the fundamental group of the manifold. New connections between the groups $LP_*$, the Novikov–Wall groups, and the splitting obstruction groups are established.

[1] Wall C. T. C., Surgery on compact manifolds, Academic Press, London, 1970 | MR

[2] Ranicki A. A., Exact sequences in the algebraic theory of surgery, Matem. Notes, 26, Princeton, 1981 | MR | Zbl

[3] Browder W., Livesay G. R., “Fixed point free involutions on homotopy spheres”, Bull. Amer. Math. Soc., 73 (1967), 242–245 | DOI | MR | Zbl

[4] Lopez de Medrano S., Involutions on manifolds, Springer-Verlag, Berlin, 1971 | MR | Zbl

[5] Cappell S. E., Shaneson J. L., “Pseudo-free actions”, Lecture Notes in Math., 763, 1979, 395–447 | MR | Zbl

[6] Kharshiladze A. F., “Perestroika mnogoobrazii s konechnymi fundamentalnymi gruppami”, UMN, 42:4 (1987), 55–85 | MR | Zbl

[7] Muranov Yu. V., Kharshiladze A. F., “Gruppy Braudera–Livsi abelevykh $2$-grupp”, Matem. sb., 181:8 (1990), 1061–1098 | MR | Zbl

[8] Hambleton I., Milgram R. J., Taylor L., Williams B., “Surgery with finite fundamental group”, Proc. London Math. Soc., 56 (1988), 349–379 | DOI | MR | Zbl

[9] Akhmetev P. M., “Rasscheplenie gomotopicheskikh ekvivalentnostei vdol odnostoronnego podmnogoobraziya korazmernosti $1$”, Izv. AN SSSR. Ser. matem., 51:2 (1987), 211–241 | MR | Zbl

[10] Kharshiladze A. F., “Obobschennyi invariant Braudera–Livsi”, Izv. AN SSSR. Ser. matem., 51:2 (1987), 379–400 | MR

[11] Muranov Yu. V., “Gruppy prepyatstvii k rasschepleniyu i kvadratichnye rasshireniya antistruktur”, Izv. RAN. Ser. matem., 59:6 (1995), 107–132 | MR | Zbl

[12] Muranov Yu. V., Repovsh D., “Prepyatstviya k perestroikam po pare mnogoobrazii”, UMN, 51:4 (1996), 165–166 | MR | Zbl

[13] Ranicki A., “The $L$-theory of twisted quadratic extensions”, Canad. J. Math., 39 (1987), 345–364 | MR | Zbl

[14] Kharshiladze A. F., “Ermitova $K$-teoriya i kvadratichnye rasshireniya kolets”, Tr. MMO, 41, URSS, M., 1980, 3–36 | MR | Zbl

[15] Muranov Yu. V., “Otnositelnye gruppy Uolla i dekoratsii”, Matem. sb., 185:12 (1994), 79–100 | Zbl

[16] Wall C. T. C., “Foundations of algebraic $L$-theory”, Lecture Notes in Math., 343, 1973, 266–300 | MR | Zbl

[17] Wall C. T. C., “On the classification of Hermitian forms. VI: Group rings”, Ann. of Math., 103 (1976), 1–80 | DOI | MR | Zbl

[18] Khemblton I., Kharshiladze A. F., “Spektralnaya posledovatelnost v teorii perestroek”, Matem. sb., 183:9 (1992), 3–14 | MR

[19] Hambleton I., Ranicki A., Taylor L., “Round $L$-theory”, J. Pure Appl. Algebra, 47 (1987), 131–134 | DOI | MR