Geodesic
Discrete Connections and Difference Linear Equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 186-201
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Following earlier works, we develop here a nonstandard discrete analogue of the theory of differential-geometric $GL_{n}$-connections on triangulated manifolds. This theory is based on the interpretation of a connection as a first-order linear difference equation—the “triangle equation”—for scalar functions of vertices in simplicial complexes. This theory appeared as a byproduct of the discretization of famous completely integrable systems such as the 2D Toda lattice. A nonstandard discretization of complex analysis based on these ideas was developed earlier. Here, a complete classification theory based on the mixture of abelian and nonabelian features is given for connections on triangulated manifolds. 
@article{TM_2004_247_a12,
     author = {S. P. Novikov},
     title = {Discrete {Connections} and {Difference} {Linear} {Equations}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {186--201},
     year = {2004},
     volume = {247},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_247_a12/}
}
TY  - JOUR
AU  - S. P. Novikov
TI  - Discrete Connections and Difference Linear Equations
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2004
SP  - 186
EP  - 201
VL  - 247
UR  - http://geodesic.mathdoc.fr/item/TM_2004_247_a12/
LA  - ru
ID  - TM_2004_247_a12
ER  - 
%0 Journal Article
%A S. P. Novikov
%T Discrete Connections and Difference Linear Equations
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2004
%P 186-201
%V 247
%U http://geodesic.mathdoc.fr/item/TM_2004_247_a12/
%G ru
%F TM_2004_247_a12
S. P. Novikov. Discrete Connections and Difference Linear Equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology and set theory, Tome 247 (2004), pp. 186-201. http://geodesic.mathdoc.fr/item/TM_2004_247_a12/

[1] Novikov S. P., “Algebraicheskie svoistva dvumernykh raznostnykh operatorov”, UMN, 52:1 (1997), 225–226 | MR | Zbl

[2] Novikov S. P., Dynnikov I. A., “Diskretnye spektralnye simmetrii malomernykh differentsialnykh operatorov i raznostnykh operatorov na pravilnykh reshetkakh i dvumernykh mnogoobraziyakh”, UMN, 52:5 (1997), 175–234 | MR | Zbl

[3] Dynnikov I. A., Novikov S. P., “Preobrazovaniya Laplasa i simplitsialnye svyaznosti”, UMN, 52:6 (1997), 157–158 | MR | Zbl

[4] Dynnikov I. A., Novikov S. P., “Geometry of the triangle equation on two-manifolds”, Moscow Math. J., 3 (2003), 419–438 | MR | Zbl

[5] Joswig M., Projectivities in simplicial complexes and colorings of simple polytopes, , 2001 arXiv: /math.CO/0102186 | MR