Geodesic
Browder–Livesay groups for Abelian 2-groups
Sbornik. Mathematics, Tome 70 (1991) no. 2, pp. 499-540 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The authors compute all the Browder–Livesay groups of an arbitrary finite abelian 2-group with an arbitrary orientation character and any subgroup of index 2. Browder–Livesay groups are obstruction groups for the problem of splitting homotopy equivalences of manifolds along one-sided submanifolds of codimension 1. All the connections with the Wall groups of abelian 2-groups which can be expressed by two-row diagrams are uncovered. 
@article{SM_1991_70_2_a10,
     author = {Yu. V. Muranov and A. F. Kharshiladze},
     title = {Browder{\textendash}Livesay groups for {Abelian} 2-groups},
     journal = {Sbornik. Mathematics},
     pages = {499--540},
     year = {1991},
     volume = {70},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1991_70_2_a10/}
}
TY  - JOUR
AU  - Yu. V. Muranov
AU  - A. F. Kharshiladze
TI  - Browder–Livesay groups for Abelian 2-groups
JO  - Sbornik. Mathematics
PY  - 1991
SP  - 499
EP  - 540
VL  - 70
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1991_70_2_a10/
LA  - en
ID  - SM_1991_70_2_a10
ER  - 
%0 Journal Article
%A Yu. V. Muranov
%A A. F. Kharshiladze
%T Browder–Livesay groups for Abelian 2-groups
%J Sbornik. Mathematics
%D 1991
%P 499-540
%V 70
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1991_70_2_a10/
%G en
%F SM_1991_70_2_a10
Yu. V. Muranov; A. F. Kharshiladze. Browder–Livesay groups for Abelian 2-groups. Sbornik. Mathematics, Tome 70 (1991) no. 2, pp. 499-540. http://geodesic.mathdoc.fr/item/SM_1991_70_2_a10/

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

[2] Kharshiladze A. F., “Prepyatstviya k perestroikam dlya gruppy $(\pi\times Z_2)$”, Matem. zametki, 16:5 (1974), 823–832 | Zbl

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

[4] Ranicki A., $L$-theory of twisted quadratic extensions. Appendix 4, Preprint, Princeton, 1981 | MR | Zbl

[5] Hambleton I., Taylor L., Williams B., “An introduction to the maps between surgery obstruction groups”, Algebraic Topology, Aarhus, 1982; Lect. Notes in Math., 1051 (1984), 49–127 | DOI | MR | Zbl

[6] Kharshiladze A. F., “Iterirovannye invarianty Braudera-Livsi i uzing problema”, Matem. zametki, 41:4 (1987), 557–563 | MR | Zbl

[7] Kharshiladze A. F., “Gladkie i kusochno-lineinye struktury na proizvedeniyakh proektivnykh prostranstv”, Izv. AN SSSR. Ser. matem., 47:2 (1983), 366–383 | MR | Zbl

[8] Kharshiladze A. F., “Perestroika mnogoobrazii s konechnymi fundamentalnymi gruppami”, UMN, 42:4 (1987), 56–85 | MR

[9] Wall C. T. C., “Foundations of algebraic $L$-theory”, Lect. Notes in Math., 343 (1973), 266–300 | DOI | MR | Zbl

[10] Wall C. T. C., “On the axiomatic foundations of the theory of hermitian forms”, Proc. Camb. Phil. Soc., 67 (1970), 243–250 | DOI | MR | Zbl

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

[12] Muranov Yu. V., “Prepyatstviya k perestroikam dvulistnykh nakrytii”, Matem. sb., 131(173) (1986), 347–356 | MR | Zbl

[13] Muranov Yu. V., Kharshiladze A. F., “Prepyatstviya k rasschepleniyu vdol odnostoronnikh podmnogoobrazii”, Izv. AN BSSR, 1988, no. 4, 25–30 | MR | Zbl

[14] Wall C. T. C., “Some $L$-groups of finite groups”, Bull. Amer. Math. Soc., 79 (1973), 526–529 | DOI | MR | Zbl

[15] Cappell S., Shaneson J., “Pseudo-free actions on homotopy spheres”, Lect. Notes in Math., 763 (1979), 397–447

[16] Muranov Yu. V., “O nerealizuemosti zamknutymi mnogoobraziyami”, Tez. MTK, Baku, 1987, S. 209 | Zbl

[17] Hambleton I., Milgram R. J., Taylor L., Williams B., Surgery with finite fundamental group, Preprint, McMaster University, 1986 | MR

[18] Hambleton I., “Surgery on closed manifolds”, Baku International Topological Conference, 1987