Geodesic
Euler structures, nonsingular vector fields, and torsions of Reidemeister type
Izvestiya. Mathematics, Tome 34 (1990) no. 3, pp. 627-662 
V. G. Turaev. Euler structures, nonsingular vector fields, and torsions of Reidemeister type. Izvestiya. Mathematics, Tome 34 (1990) no. 3, pp. 627-662. http://geodesic.mathdoc.fr/item/IM2_1990_34_3_a5/
@article{IM2_1990_34_3_a5,
     author = {V. G. Turaev},
     title = {Euler structures, nonsingular vector fields, and torsions of {Reidemeister} type},
     journal = {Izvestiya. Mathematics},
     pages = {627--662},
     year = {1990},
     volume = {34},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_34_3_a5/}
}
TY  - JOUR
AU  - V. G. Turaev
TI  - Euler structures, nonsingular vector fields, and torsions of Reidemeister type
JO  - Izvestiya. Mathematics
PY  - 1990
SP  - 627
EP  - 662
VL  - 34
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1990_34_3_a5/
LA  - en
ID  - IM2_1990_34_3_a5
ER  - 
%0 Journal Article
%A V. G. Turaev
%T Euler structures, nonsingular vector fields, and torsions of Reidemeister type
%J Izvestiya. Mathematics
%D 1990
%P 627-662
%V 34
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1990_34_3_a5/
%G en
%F IM2_1990_34_3_a5

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

Combinatorial analogues of nonsingular vector fields on manifolds, so-called Euler structures, are introduced and studied. A refinement of Reidemeister's construction of torsion is proposed that gives new invariants of nonsingular vector fields and Euler structures. Bibliography: 12 titles.

[1] Boltyanskii V. G., “Gomotopicheskaya klassifikatsiya vektornykh polei”, Dokl. AN SSSR, 118:1 (1958), 13–16 | MR

[2] Franz W., “Torsionideale, Torsionklassen und Torsion”, J. Reine Angew. Math., 176 (1937), 113–124

[3] Halperin S., Toledo D., “Stiefel–Whitney homology classes”, Ann. Math., 96:3 (1972), 511–525 | DOI | MR | Zbl

[4] Milnor J. W., “A duality theorem for Reidemeister torsion”, Ann. Math., 76:1 (1962), 137–147 | DOI | MR | Zbl

[5] Milnor J. W., “Spin structures on manifolds”, Enseign. Math., 9:3 (1963), 198–203 | MR | Zbl

[6] Milnor Dzh., Kruchenie Uaitkheda, Matematika, 11, no. 1, 1967 | MR

[7] Munkres J. R., Elementary differential topology, Ann. Math. Studies, 54, 1966 | MR | Zbl

[8] Ray D. B., Singer I. M., “$R$-torsion and the Laplasian on Reimannian Manifolds”, Adv. Math., 7 (1971), 145–210 | DOI | MR | Zbl

[9] Rurk K., Sanderson B., Vvedenie v kusochno-lineinuyu topologiyu, Mir, M., 1974 | MR

[10] Turaev V. G., “Kruchenie Raidemaistera v teorii uzlov”, UMN, 41:1(246) (1986), 97–147 | MR | Zbl

[11] Turaev V. G., K topologicheskoi klassifikatsii geometricheskikh trekhmernykh mnogoobrazii, Preprint R-7-86, LOMI, L., 1986 | MR

[12] Turaev V. G., Towards the topological classification of geometric $3$-manifolds, Lect. Notes Math., 1987 | MR