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Extending $T^p$ automorphisms over $\mathbb{R}^{p+2}$ and realizing DE attractors
1. | School of Mathematical Sciences, Peking University, Beijing, 100871, China, China |
2. | Department of Mathematics, 970 Evans Hall, University of California, Berkeley, CA 94720-3840, United States, United States |
References:
[1] |
Hans G. Bothe, The ambient structure of expanding attractors. II. Solenoids in 3-manifolds, Math. Nachr., 112 (1983), 69-102.
doi: 10.1002/mana.19831120105. |
[2] |
Fan Ding, Yi Liu, Shicheng Wang and Jiangang Yao, Spin structure and codimension-two homeomorphism extension,, preprint, ().
|
[3] |
Fan Ding, Jianzhong Pan, Shicheng Wang and Jiangang Yao, Only rational homology spheres admit $\Omega(f)$ to be union of DE attractors, Ergodic Theory Dynam. Systems, 30 (2010), 1399-1417.
doi: 10.1017/S014338570900073X. |
[4] |
Karel Dekimpe, Michał Sadowski and Andrzej Szczepański, Spin structures on flat manifolds, Monatsh. Math., 148 (2006), 283-296. |
[5] |
David Epstein and Michael Shub, Expanding endomorphisms of flat manifolds, Topol., 7 (1968), 139-141.
doi: 10.1016/0040-9383(68)90022-0. |
[6] |
Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math., 53 (1981), 53-73. |
[7] |
André Haefliger, Plongements différentiables dans le domaine stable, (French),, Comment. Math. Helv., 37 (): 155.
|
[8] |
Morris W. Hirsch, "Differential Topology," Graduate Texts in Mathematics, No. 33, Springer-Verlag, New York-Heidelberg, 1976. |
[9] |
Boju Jiang, Yi Ni and Shicheng Wang, 3-manifolds that admit knotted solenoids as attractors, Trans. Amer. Math. Soc., 356 (2004), 4371-4382.
doi: 10.1090/S0002-9947-04-03503-2. |
[10] |
Boju Jiang, Shicheng Wang and Hao Zheng, No embeddings of solenoids into surfaces, Proc. Amer. Math. Soc., 136 (2008), 3697-3700.
doi: 10.1090/S0002-9939-08-09340-4. |
[11] |
John W. Milnor and James D. Stasheff, "Characteristic Classes," Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1974. |
[12] |
Morris Newman, "Integral Matrices," Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. |
[13] |
Stephen Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
doi: 10.1090/S0002-9904-1967-11798-1. |
[14] |
Thomas E. Stewart, On groups of diffeomorphisms, Proc. Amer. Math. Soc., 11 (1960), 559-563.
doi: 10.1090/S0002-9939-1960-0120651-6. |
[15] |
Wen-tsün Wu, On the isotopy of $C^r$-manifolds of dimension $n$ in euclidean $(2n+1)$-space, Sci. Record (N.S.), 2 (1958), 271-275. |
show all references
References:
[1] |
Hans G. Bothe, The ambient structure of expanding attractors. II. Solenoids in 3-manifolds, Math. Nachr., 112 (1983), 69-102.
doi: 10.1002/mana.19831120105. |
[2] |
Fan Ding, Yi Liu, Shicheng Wang and Jiangang Yao, Spin structure and codimension-two homeomorphism extension,, preprint, ().
|
[3] |
Fan Ding, Jianzhong Pan, Shicheng Wang and Jiangang Yao, Only rational homology spheres admit $\Omega(f)$ to be union of DE attractors, Ergodic Theory Dynam. Systems, 30 (2010), 1399-1417.
doi: 10.1017/S014338570900073X. |
[4] |
Karel Dekimpe, Michał Sadowski and Andrzej Szczepański, Spin structures on flat manifolds, Monatsh. Math., 148 (2006), 283-296. |
[5] |
David Epstein and Michael Shub, Expanding endomorphisms of flat manifolds, Topol., 7 (1968), 139-141.
doi: 10.1016/0040-9383(68)90022-0. |
[6] |
Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math., 53 (1981), 53-73. |
[7] |
André Haefliger, Plongements différentiables dans le domaine stable, (French),, Comment. Math. Helv., 37 (): 155.
|
[8] |
Morris W. Hirsch, "Differential Topology," Graduate Texts in Mathematics, No. 33, Springer-Verlag, New York-Heidelberg, 1976. |
[9] |
Boju Jiang, Yi Ni and Shicheng Wang, 3-manifolds that admit knotted solenoids as attractors, Trans. Amer. Math. Soc., 356 (2004), 4371-4382.
doi: 10.1090/S0002-9947-04-03503-2. |
[10] |
Boju Jiang, Shicheng Wang and Hao Zheng, No embeddings of solenoids into surfaces, Proc. Amer. Math. Soc., 136 (2008), 3697-3700.
doi: 10.1090/S0002-9939-08-09340-4. |
[11] |
John W. Milnor and James D. Stasheff, "Characteristic Classes," Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1974. |
[12] |
Morris Newman, "Integral Matrices," Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. |
[13] |
Stephen Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
doi: 10.1090/S0002-9904-1967-11798-1. |
[14] |
Thomas E. Stewart, On groups of diffeomorphisms, Proc. Amer. Math. Soc., 11 (1960), 559-563.
doi: 10.1090/S0002-9939-1960-0120651-6. |
[15] |
Wen-tsün Wu, On the isotopy of $C^r$-manifolds of dimension $n$ in euclidean $(2n+1)$-space, Sci. Record (N.S.), 2 (1958), 271-275. |
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