Projective splitting obstruction groups for one-sided submanifolds
Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1465-1485 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A geometric diagram of groups, which consists of groups equipped with geometric antistructures, is a natural generalization of the square of fundamental groups arising in the splitting problem for a one-sided submanifold. In the present paper the groups $LS_*$ and $LP_*$ of such diagrams are defined and the properties of these groups are described. Methods for the computation of $LS_*^p$, $LP_*^p$-groups and natural maps in diagrams of exact sequences are developed in the case of a geometric diagram of finite 2-groups.
@article{SM_1999_190_10_a3,
     author = {Yu. V. Muranov and I. Hambleton},
     title = {Projective splitting obstruction groups for one-sided submanifolds},
     journal = {Sbornik. Mathematics},
     pages = {1465--1485},
     year = {1999},
     volume = {190},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_10_a3/}
}
TY  - JOUR
AU  - Yu. V. Muranov
AU  - I. Hambleton
TI  - Projective splitting obstruction groups for one-sided submanifolds
JO  - Sbornik. Mathematics
PY  - 1999
SP  - 1465
EP  - 1485
VL  - 190
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/SM_1999_190_10_a3/
LA  - en
ID  - SM_1999_190_10_a3
ER  - 
%0 Journal Article
%A Yu. V. Muranov
%A I. Hambleton
%T Projective splitting obstruction groups for one-sided submanifolds
%J Sbornik. Mathematics
%D 1999
%P 1465-1485
%V 190
%N 10
%U http://geodesic.mathdoc.fr/item/SM_1999_190_10_a3/
%G en
%F SM_1999_190_10_a3
Yu. V. Muranov; I. Hambleton. Projective splitting obstruction groups for one-sided submanifolds. Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1465-1485. http://geodesic.mathdoc.fr/item/SM_1999_190_10_a3/

[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, Princeton Univ. Press, 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] Hambleton I., “Projective surgery obstructions on closed manifolds”, Lecture Notes in Math., 967, 1982, 101–131 | MR | Zbl

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

[8] Kharshiladze A. F., “Obobschennyi invariant Braudera–Livsi”, Izv. AN SSSR. Ser. matem., 51:2 (1987), 379–401 | MR | Zbl

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

[10] Muranov Yu. V., Repovsh D., “Gruppy prepyatstvii k perestroikam i rasschepleniyam dlya pary mnogoobrazii”, Matem. sb., 188:3 (1997), 127–142 | MR | Zbl

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

[12] Hambleton I., Taylor L. R., Williams B., “An introduction to maps between surgery obstruction groups”, Lecture Notes in Math., 1051, 1984, 49–127 | MR | Zbl

[13] Hambleton I., Taylor L. R., Williams B., “Detection theorems for K-theory and L-theory”, J. Pure Appl. Algebra, 63 (1990), 247–299 | DOI | MR | Zbl

[14] Wall C. T. C., “On the classification of Hermitian forms. VI: Group rings”, Ann. of Math. (2), 103 (1976), 1–80 | DOI | MR | Zbl

[15] Hambleton I., Madsen I., “On the computation of the projective surgery obstruction groups”, K-Theory, 7:6 (1993), 537–574 | DOI | MR | Zbl

[16] Wall C. T. C., “Formulae for surgery obstructions”, Topology, 15 (1976), 189–210 | DOI | MR | Zbl

[17] Novikov S. P., “Algebraicheskaya konstruktsiya i svoistva ermitovykh analogov K-teorii dlya kolets s involyutsiei”, Izv. AN SSSR. Ser. matem., 34:2 (1970), 253–288 | Zbl

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

[19] Wall C. T. C., “On the axiomatic foundation of the theory of Hermitian forms”, Proc. Cambridge Philos. Soc., 67 (1970), 243–250 | DOI | MR | Zbl

[20] Hambleton I., Ranicki A., Taylor L., “Round L-theory”, J. Pure Appl. Algebra, 47 (1987), 131–154 | DOI | MR | Zbl

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