Varieties of representations and their cohomology-jump subvarieties for knot groups
Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 187-209 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper studies the spaces of representations of knot groups into a linear group $\mathrm{GL}_n(\mathbb{C})$, their categorical factor-spaces (i.e., the spaces of all characters of the representations), and their cohomology-jump subspaces. Connections are established between the latter and the spaces of representations of dimension one greater. A complete description is given of these spaces for 2-bridge knots.
@article{SM_1994_78_1_a11,
     author = {Le Tu Quoc Thang},
     title = {Varieties of representations and their cohomology-jump subvarieties for knot groups},
     journal = {Sbornik. Mathematics},
     pages = {187--209},
     year = {1994},
     volume = {78},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_1_a11/}
}
TY  - JOUR
AU  - Le Tu Quoc Thang
TI  - Varieties of representations and their cohomology-jump subvarieties for knot groups
JO  - Sbornik. Mathematics
PY  - 1994
SP  - 187
EP  - 209
VL  - 78
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1994_78_1_a11/
LA  - en
ID  - SM_1994_78_1_a11
ER  - 
%0 Journal Article
%A Le Tu Quoc Thang
%T Varieties of representations and their cohomology-jump subvarieties for knot groups
%J Sbornik. Mathematics
%D 1994
%P 187-209
%V 78
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1994_78_1_a11/
%G en
%F SM_1994_78_1_a11
Le Tu Quoc Thang. Varieties of representations and their cohomology-jump subvarieties for knot groups. Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 187-209. http://geodesic.mathdoc.fr/item/SM_1994_78_1_a11/

[1] Novikov S. P., “Blokhovskie gomologii, kriticheskie tochki funktsii i $1$-form”, DAN SSSR, 287:6 (1986) | MR | Zbl

[2] Le Ty Kuok Tkhang, “Mnogoobraziya predstavlenii i ikh podmnogoobraziya podskokov gomologii dlya nekotorykh klassov grupp uzlov”, UMN, 46:2 (1991), 223–224 | MR | Zbl

[3] Alaniya L., “O mnogoobrazii tipa Aleksandera”, UMN (to appear)

[4] Burde G., Zieschang H., Knots, Walter de Gruyter, Berlin, 1985 | MR | Zbl

[5] Crowell R., Fox R., Introduction to knot theory, Ginn and Company, N.Y., 1963 | MR | Zbl

[6] Lubotzky A., Magid A. R., “Varieties of representations of finitely generated groups”, Memouris Amer. Math. Soc., 58:336 (1985), 1–110 | MR

[7] Culler M., Shallen P., “Varieties of group representations and splitting of $3$-manifolds”, Ann. Math. Ser. 2, 117:1 (1983), 109–146 | DOI | MR | Zbl

[8] Riley R., “Non-abelian representations of $2$-bridge knot groups”, Quart. J. Math. Ser. 2, 35:138 (1984), 191–208 | DOI | MR | Zbl

[9] Whittemore, “On representation of the group of listing knot by subgroups of SL”, Proc. Amer. Math. Soc., 40:2 (1973), 318–322

[10] Dedonne Dzh., Kerrol Dzh., Mamford D., Geometricheskaya teoriya invariantov, Mir, M., 1974 | MR

[11] Lindon R., Shupp P., Kombinatornaya teoriya grupp, Mir, M., 1980 | MR

[12] Turaev V. G., “The Yang-Baxter equations and invariants of links”, Inv. Math., 92 (1988), 527–553 | DOI | MR | Zbl