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On the rigidity of Weyl chamber flows and Schur multipliers as topological groups
1. | Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States |
References:
[1] |
D. Damjanović, Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions, J. Mod. Dyn., 1 (2007), 665-688.
doi: 10.3934/jmd.2007.1.665. |
[2] |
D. Damjanović and A. Katok, Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic $\mathbbR^k$ actions, Discrete Contin. Dyn. Syst., 13 (2005), 985-1005.
doi: 10.3934/dcds.2005.13.985. |
[3] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions I. KAM method and $\mathbbZ^k$ actions on the torus, Ann. of Math. (2), 172 (2010), 1805-1858.
doi: 10.4007/annals.2010.172.1805. |
[4] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II: The geometric method and restrictions of Weyl chamber flows on $SL$$(n,\mathbbR)$$/$$\Gamma$, Int. Math. Res. Not. IMRN, (2011), 4405-4430.
doi: 10.1093/imrn/rnq252. |
[5] |
V. V. Deodhar, On central extensions of rational points of algebraic groups, Amer. J. Math., 100 (1978), 303-386.
doi: 10.2307/2373853. |
[6] |
J. L. Dupont, W. Parry and C.-H. Sah, Homology of classical Lie groups made discrete. II. $H_2,H_3,$ and relations with scissors congruences, J. Algebra, 113 (1988), 215-260.
doi: 10.1016/0021-8693(88)90191-3. |
[7] |
A. M. Gleason and R. S. Palais, On a class of transformation groups, Amer. J. Math., 79 (1957), 631-648.
doi: 10.2307/2372567. |
[8] |
M. Grayson, C. Pugh and M. Shub, Stably ergodic diffeomorphisms, Ann. of Math. (2), 140 (1994), 295-329.
doi: 10.2307/2118602. |
[9] |
R. Hartshorne, ed., Algebraic Geometry, Corrected reprint of the 1975 original, Proceedings of Symposia in Pure Mathematics, Vol. 29, American Mathematical Society, Providence, R.I., 1979. |
[10] |
A. Katok and R. J. Spatzier, Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions, Tr. Mat. Inst. Steklova, 216 (1997), Din. Sist. i Smezhnye Vopr., 292-319. |
[11] |
A. Katok, V. Niţică and A. Török, Non-abelian cohomology of abelian Anosov actions, Ergodic Theory Dynam. Systems, 20 (2000), 259-288.
doi: 10.1017/S0143385700000122. |
[12] |
G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 17, Springer-Verlag, Berlin, 1991. |
[13] |
J. Milnor, Introduction to Algebraic $K$-Theory, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. |
[14] |
S. A. Morris, Free products of topological groups, Bull. Austral. Math. Soc., 4 (1971), 17-29.
doi: 10.1017/S0004972700046219. |
[15] |
E. T. Ordman, Free products of topological groups which are $k_{\omega }$-spaces, Trans. Amer. Math. Soc., 191 (1974), 61-73. |
[16] |
C. Pugh and M. Shub, Stably ergodic dynamical systems and partial hyperbolicity, J. Complexity, 13 (1997), 125-179.
doi: 10.1006/jcom.1997.0437. |
[17] |
C. Pugh, M. Shub and A. Wilkinson, Hölder foliations, revisited, J. Mod. Dyn., 6 (2012), 79-120.
doi: 10.3934/jmd.2012.6.79. |
[18] |
C. H. Sah and J. B. Wagoner, Second homology of Lie groups made discrete, Comm. Algebra, 5 (1977), 611-642.
doi: 10.1080/00927877708822184. |
[19] |
Z. Wang, Local rigidity of partially hyperbolic actions: Twisted symmetric space examples, preprint. |
[20] |
Z. J. Wang, Local rigidity of partially hyperbolic actions, J. Mod. Dyn., 4 (2010), 271-327.
doi: 10.3934/jmd.2010.4.271. |
[21] |
Z. J. Wang, New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions, J. Mod. Dyn., 4 (2010), 585-608.
doi: 10.3934/jmd.2010.4.585. |
show all references
References:
[1] |
D. Damjanović, Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions, J. Mod. Dyn., 1 (2007), 665-688.
doi: 10.3934/jmd.2007.1.665. |
[2] |
D. Damjanović and A. Katok, Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic $\mathbbR^k$ actions, Discrete Contin. Dyn. Syst., 13 (2005), 985-1005.
doi: 10.3934/dcds.2005.13.985. |
[3] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions I. KAM method and $\mathbbZ^k$ actions on the torus, Ann. of Math. (2), 172 (2010), 1805-1858.
doi: 10.4007/annals.2010.172.1805. |
[4] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II: The geometric method and restrictions of Weyl chamber flows on $SL$$(n,\mathbbR)$$/$$\Gamma$, Int. Math. Res. Not. IMRN, (2011), 4405-4430.
doi: 10.1093/imrn/rnq252. |
[5] |
V. V. Deodhar, On central extensions of rational points of algebraic groups, Amer. J. Math., 100 (1978), 303-386.
doi: 10.2307/2373853. |
[6] |
J. L. Dupont, W. Parry and C.-H. Sah, Homology of classical Lie groups made discrete. II. $H_2,H_3,$ and relations with scissors congruences, J. Algebra, 113 (1988), 215-260.
doi: 10.1016/0021-8693(88)90191-3. |
[7] |
A. M. Gleason and R. S. Palais, On a class of transformation groups, Amer. J. Math., 79 (1957), 631-648.
doi: 10.2307/2372567. |
[8] |
M. Grayson, C. Pugh and M. Shub, Stably ergodic diffeomorphisms, Ann. of Math. (2), 140 (1994), 295-329.
doi: 10.2307/2118602. |
[9] |
R. Hartshorne, ed., Algebraic Geometry, Corrected reprint of the 1975 original, Proceedings of Symposia in Pure Mathematics, Vol. 29, American Mathematical Society, Providence, R.I., 1979. |
[10] |
A. Katok and R. J. Spatzier, Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions, Tr. Mat. Inst. Steklova, 216 (1997), Din. Sist. i Smezhnye Vopr., 292-319. |
[11] |
A. Katok, V. Niţică and A. Török, Non-abelian cohomology of abelian Anosov actions, Ergodic Theory Dynam. Systems, 20 (2000), 259-288.
doi: 10.1017/S0143385700000122. |
[12] |
G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 17, Springer-Verlag, Berlin, 1991. |
[13] |
J. Milnor, Introduction to Algebraic $K$-Theory, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. |
[14] |
S. A. Morris, Free products of topological groups, Bull. Austral. Math. Soc., 4 (1971), 17-29.
doi: 10.1017/S0004972700046219. |
[15] |
E. T. Ordman, Free products of topological groups which are $k_{\omega }$-spaces, Trans. Amer. Math. Soc., 191 (1974), 61-73. |
[16] |
C. Pugh and M. Shub, Stably ergodic dynamical systems and partial hyperbolicity, J. Complexity, 13 (1997), 125-179.
doi: 10.1006/jcom.1997.0437. |
[17] |
C. Pugh, M. Shub and A. Wilkinson, Hölder foliations, revisited, J. Mod. Dyn., 6 (2012), 79-120.
doi: 10.3934/jmd.2012.6.79. |
[18] |
C. H. Sah and J. B. Wagoner, Second homology of Lie groups made discrete, Comm. Algebra, 5 (1977), 611-642.
doi: 10.1080/00927877708822184. |
[19] |
Z. Wang, Local rigidity of partially hyperbolic actions: Twisted symmetric space examples, preprint. |
[20] |
Z. J. Wang, Local rigidity of partially hyperbolic actions, J. Mod. Dyn., 4 (2010), 271-327.
doi: 10.3934/jmd.2010.4.271. |
[21] |
Z. J. Wang, New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions, J. Mod. Dyn., 4 (2010), 585-608.
doi: 10.3934/jmd.2010.4.585. |
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