# The associated map of the nonabelian Gauss-Manin connection

Open Mathematics (2012)

- Volume: 10, Issue: 4, page 1407-1421
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topTing Chen. "The associated map of the nonabelian Gauss-Manin connection." Open Mathematics 10.4 (2012): 1407-1421. <http://eudml.org/doc/269412>.

@article{TingChen2012,

abstract = {The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. The result turns out to be intimately related to the quadratic part of the Hitchin map.},

author = {Ting Chen},

journal = {Open Mathematics},

keywords = {Gauss-Manin connection; Isomonodromy flow; Hogde filtration; Hitchin map; isomonodromy flow; hogde filtration},

language = {eng},

number = {4},

pages = {1407-1421},

title = {The associated map of the nonabelian Gauss-Manin connection},

url = {http://eudml.org/doc/269412},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Ting Chen

TI - The associated map of the nonabelian Gauss-Manin connection

JO - Open Mathematics

PY - 2012

VL - 10

IS - 4

SP - 1407

EP - 1421

AB - The Gauss-Manin connection for nonabelian cohomology spaces is the isomonodromy flow. We write down explicitly the vector fields of the isomonodromy flow and calculate its induced vector fields on the associated graded space of the nonabelian Hogde filtration. The result turns out to be intimately related to the quadratic part of the Hitchin map.

LA - eng

KW - Gauss-Manin connection; Isomonodromy flow; Hogde filtration; Hitchin map; isomonodromy flow; hogde filtration

UR - http://eudml.org/doc/269412

ER -

## References

top- [1] Ben-Zvi D., Frenkel E., Geometric realization of the Segal-Sugawara construction, In: Topology, Geometry and Quantum Field Theory, London Math. Soc. Lecture Note Ser., 308, Cambridge University Press, Cambridge, 2004, 46–97 http://dx.doi.org/10.1017/CBO9780511526398.006 Zbl1170.17303
- [2] Griffiths P.A., Periods of integrals on algebraic manifolds II. (Local study of the period mapping), Amer. J. Math., 1968, 90(5), 805–865 http://dx.doi.org/10.2307/2373485 Zbl0183.25501
- [3] Hitchin N.J., The self-duality equations on a Riemann surface, Proc. London Math. Soc., 1987, 55(1), 59–126 http://dx.doi.org/10.1112/plms/s3-55.1.59 Zbl0634.53045
- [4] Inaba M., Iwasaki K., Saito M.-H., Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI, Part I, Publ. Res. Inst. Math. Sci., 2006, 42(4), 987–1089 http://dx.doi.org/10.2977/prims/1166642194 Zbl1127.34055
- [5] Markman E., Spectral curves and integrable systems, Compositio Math., 1994, 93(3), 255–290 Zbl0824.14013
- [6] Mumford D., Projective invariants of projective structures and applications, In: Proc. Internat. Congr. Mathematicians, Stockholm, 1962, Inst. Mittag-Leffler, Djursholm, 1963, 526–530 Zbl0154.20702
- [7] Simpson C., The Hodge filtration on nonabelian cohomology, In: Algebraic Geometry, Santa Cruz, 1995, Proc. Sympos. Pure Math., 62(2), American Mathematical Society, Providence, 1997, 217–281

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.