The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces

Michael Kapovich; John J. Millson

Compositio Mathematica (1996)

  • Volume: 103, Issue: 3, page 287-317
  • ISSN: 0010-437X

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Kapovich, Michael, and Millson, John J.. "The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces." Compositio Mathematica 103.3 (1996): 287-317. <http://eudml.org/doc/90473>.

@article{Kapovich1996,
author = {Kapovich, Michael, Millson, John J.},
journal = {Compositio Mathematica},
keywords = {relative deformation; differential graded Lie algebra; mechanical linkage; representation variety},
language = {eng},
number = {3},
pages = {287-317},
publisher = {Kluwer Academic Publishers},
title = {The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces},
url = {http://eudml.org/doc/90473},
volume = {103},
year = {1996},
}

TY - JOUR
AU - Kapovich, Michael
AU - Millson, John J.
TI - The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 103
IS - 3
SP - 287
EP - 317
LA - eng
KW - relative deformation; differential graded Lie algebra; mechanical linkage; representation variety
UR - http://eudml.org/doc/90473
ER -

References

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  3. [BM] Buchweitz, R.O. and Millson, J.J.: CR-geometry and deformations of isolated singularities, to appear in the Memoirs of the A.M.S. Zbl0871.32023MR1355712
  4. [BZ] Brylinski, J.L. and Zucker, S.: An overview of recent advances in Hodge theory, Several Complex Variables, IV, Encyclopedia of Math. Sciences, 69, Springer-Verlag. Zbl0793.14005
  5. [Co] Connelly, R.: The rigidity of certain cabled frameworks and the second order rigidity of arbitrarily triangulated convex surfaces, Adv. Math.37 (1980), 272-299. Zbl0446.51012MR591730
  6. [DM] Deligne, P. and Mostow, G.D.: Monodromy of hypergeometric functions and non-lattice integral monodromy. IHES63 (1986), 5-89. Zbl0615.22008MR849651
  7. [GM1] Goldman, W.M. and Millson, J.J.: The deformation theory of fundamental groups of compact Kahler manifolds, Publ. Math. IHES67 (1988), 43-96. Zbl0678.53059MR972343
  8. [GM2] Goldman, W.M. and Millson, J.J.: The homotopy invariance of the Kuranishi space, 111. J. Math.34 (1990) 337-367. Zbl0707.32004MR1046568
  9. [H] Hain, R.: in preparation. 
  10. [HS] Hochschild, G.P. and Serre, J.P.: Cohomology of group extensions, T.A.M.S.74 (1953), 110-134. Zbl0050.02104MR52438
  11. [JM] Johnson, D. and Millson, J.J.: Deformation spaces associated to compact hyperbolic manifolds, in Discrete Groups in Geometry and Analysis, Papers in Honor of G. D. Mostow on His Sixtieth Birthday, Progr. Math.67 (1987), Birkhäuser, 48-106. Zbl0664.53023MR900823
  12. [KM1] Kapovich, M. and Millson, J.J.: Hodge theory and the art of paper folding, preprint. Zbl0961.32026MR1442490
  13. [KM2] Kapovich, M. and Millson, J.J.: Bending deformations of representations of fundamental groups of two complexes of groups, in preparation. 
  14. [KM3] Kapovich, M. and Millson, J.J.: On the deformation theory of representations of fundamental groups of compact hyperbolic 3-manifolds, to appear in Topology. Zbl0855.32013MR1404926
  15. [LM] Lubotzky, A. and Magid, A.: Varieties of representations of finitely-generated groups, Memoirs of the A.M.S.58, 1985. Zbl0598.14042MR818915
  16. [M] Millson, J.J.: Rational homotopy theory and deformation problems from algebraic geometry, Proc. Int. Congress of Math., Kyoto (1990), 549-558. Zbl0761.32011MR1159242
  17. [Sc] Schlessinger, M.: Functors of Artin rings, T.A.M.S.130 (1966), 208-222. Zbl0167.49503MR217093
  18. [Sch] Scharlau, W.: Quadratic and Hermitian Forms, Grundlehren der mathematischen Wissenschaften, 270 (1985), Springer-Verlag. Zbl0584.10010MR770063
  19. [Th] Thurston, W.P.: The Geometry and Topology of Three-Manifolds, Princeton University notes. 

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