On the Cohomology Groups of Complexes of Homogeneous Forms on Loop Spaces of Smooth Manifolds

O. I. Mokhov

Funkcionalʹnyj analiz i ego priloženiâ, Tome 32 (1998) no. 3, pp. 22-34.

Bibliographie

[1] Mokhov O. I., “O kompleksakh odnorodnykh form na prostranstvakh petel gladkikh mnogoobrazii i ikh gruppakh kogomologii”, UMN, 51:2 (1996), 141–142 | DOI | MR | Zbl

[2] Dubrovin B. A., Novikov S. P., “Gamiltonov formalizm odnomernykh sistem gidrodinamicheskogo tipa i metod usredneniya Bogolyubova–Uizema”, DAN SSSR, 270:4 (1983), 781–785 | MR | Zbl

[3] Dubrovin B. A., Novikov S. P., “Gidrodinamika slabo deformirovannykh solitonnykh reshetok. Differentsialnaya geometriya i gamiltonova teoriya”, UMN, 44:6 (1989), 29–98 | MR | Zbl

[4] Dubrovin B. A., Novikov S. P., Hydrodynamics of soliton lattices, Sov. Sci. Rev. Sec. C, Math. Phys., 9, Harwood Academic Publishers, Yverdon, 1993 | MR

[5] Tsarev S. P., “Geometriya gamiltonovykh sistem gidrodinamicheskogo tipa. Obobschennyi metod godografa”, Izv. AN SSSR, ser. matem., 54:5 (1990), 1048–1068 | MR | Zbl

[6] Maltsev A. Ya., The conservation of the Hamiltonian structures in Whitham's method of averaging, arXiv: /solv-int/9611008 | MR

[7] Maltsev A. Ya., “Usrednenie lokalnykh teoretiko-polevykh skobok Puassona”, UMN, 52:2 (1997), 177–178 | DOI | MR

[8] Mokhov O. I., Ferapontov E. V., “O nelokalnykh gamiltonovykh operatorakh gidrodinamicheskogo tipa, svyazannykh s metrikami postoyannoi krivizny”, UMN, 45:3 (1990), 191–192 | MR | Zbl

[9] Mokhov O. I., “Hamiltonian systems of hydrodynamic type and constant curvature metrics”, Phys. Lett. A, 166:3, 4 (1992), 215–216 | DOI | MR

[10] Ferapontov E. V., “Differentsialnaya geometriya nelokalnykh gamiltonovykh operatorov gidrodinamicheskogo tipa”, Funkts. analiz i ego pril., 25:3 (1991), 37–49 | MR | Zbl

[11] Mokhov O. I., Ferapontov E. V., “Gamiltonovy pary, porozhdaemye kososimmetrichnymi tenzorami Killinga na prostranstvakh postoyannoi krivizny”, Funkts. analiz i ego pril., 28:2 (1994), 60–63 | MR | Zbl

[12] Dubrovin B. A., Novikov S. P., “O skobkakh Puassona gidrodinamicheskogo tipa”, DAN SSSR, 279:2 (1984), 294–297 | MR | Zbl

[13] Potemin G. V., “O skobkakh Puassona differentsialno-geometricheskogo tipa”, DAN SSSR, 286:1 (1986), 39–42 | MR | Zbl

[14] Potemin G. V., Nekotorye voprosy differentsialnoi geometrii i algebraicheskoi geometrii v teorii solitonov, Diss. k.f.-m.n., MGU, M., 1991 | MR

[15] Doyle P. W., “Differential geometric Poisson bivectors in one space variable”, J. Math. Phys., 34:4 (1993), 1314–1338 | DOI | MR | Zbl

[16] Mokhov O. I., Nutku Y., Homogeneous Poisson brackets of Dubrovin–Novikov type and their nonlocal generalizations, Preprint, $\dot{\text{I}}$ – Marmara Research Center, Research Institute for Basic Sciences, Gebze, Turkey, 1996

[17] Ferapontov E. V., Galvão C. A. P., Mokhov O. I., Nutku Y., “Bi-Hamiltonian structure of equations of associativity in $2$-d topological field theory”, Commun. Math. Phys., 186 (1997), 649–669 | DOI | MR | Zbl

[18] Mokhov O. I., “O skobkakh Puassona tipa Dubrovina–Novikova (DN-skobki)”, Funkts. analiz i ego pril., 22:4 (1988), 92–93 | MR | Zbl

[19] Mokhov O. I., “Simplekticheskie formy na prostranstve petel i rimanova geometriya”, Funkts. analiz i ego pril., 24:3 (1990), 86–87 | MR

[20] Mokhov O. I., “Odnorodnye simplekticheskie struktury vtorogo poryadka na prostranstvakh petel i simplekticheskie svyaznosti”, Funkts. analiz i ego pril., 25:2 (1991), 65–67 | MR

[21] Mokhov O. I., “Symplectic and Poisson geometry on loop spaces of manifolds and nonlinear equations”, Topics in topology and mathematical physics, Amer. Math. Soc. Transl., ser. 2, 170, ed. S. P. Novikov, Providence, RI, 1995, 121–151 ; arXiv: /hep-th/9503076 | MR | Zbl

[22] Mokhov O. I., Simplekticheskie i puassonovy struktury na prostranstvakh petel gladkikh mnogoobrazii i integriruemye sistemy., Diss. d.f.-m.n., MIAN, M., 1996 | MR

[23] Mokhov O. I., “Two-dimensional nonlinear sigma-models and symplectic geometry on loop spaces of (pseudo)-Riemannian manifolds”, Nonlinear Evolution Equations and Dynamical Systems, Proc. 8th Internat. Workshop on Nonlinear Evolution Equations and Dynamical Systems (NEEDS'92) (July 6–17, 1992, Dubna), eds. V. Makhankov, I. Puzynin, and O. Pashaev, World Scientific Publishing, Singapore, 1993, 444–456 ; arXiv: /hep-th/9301048 | MR

[24] Mokhov O. I., “Poisson and symplectic geometry on loop spaces of smooth manifolds”, Geometry from the Pacific Rim, Proc. Pacific Rim Geometry Conference (Singapore, 1994), eds. A. J. Berrick, B. Loo, H.-Y. Wang, Walter de Gruyter Co, Berlin, 1997, 285–309 | MR | Zbl