Abstract
We show that the universal cover of an aspherical manifold whose fundamental groups has finite asymptotic dimension in sense of Gromov is hypereuclidean after crossing with some Euclidean space
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bartels A. (2003). Squeezing and higher algebraic K-theory. K-Theory 28:19–37
Bell G. and Dranishnikov A. (2001). On asymptotic dimension of groups. Algebr. Geom. Topol 1:57–71
Bell G. and Dranishnikov A. (2004). On asymptotic dimension of groups acting on trees. Geom. Dedicata 103:89–101
Carlsson G. and Goldfarb B. (2004). The integral K-theoretic Novikov conjecture for groups with finite asymptotic dimension. Invent. Math 157(2):405–418
Dranishnikov A. (2000). Asymptotic topology. Russian Math. Surveys. 55(6):71–116
Dranishnikov A. (2003). On hypersphericity of manifolds with finite asymptotic dimension. Trans. Amer. Math. Soc 355(1):155–167
Dranishnikov A. and Ferry S. (1997). On the Higson-Roe corona. Russian Math. Surveys 52(5):1017–1028
Dranishnikov A., Ferry S. and Weinberger S. (2003). Large Riemannian manifolds which are flexible. Ann. of Math 157: 919–938
Dranishnikov, A., Ferry, S. and Weinberger, S.: An etale approach to the Novikov conjecture, Preprint of MPI für Mathematik (2005)
Dranishnikov A. and Januszkiewicz T. (1999). Every Coxeter group acts amenably on a compact space. Topology Proc 24:135–141
Ferry S., Ranicki A. and Rosenberg J (eds). Novikov Conjectures, Index Theorems and Rigidity, Vol. 1, 2, London Math. Soc. Lecture Note in Ser., 226, Cambridge University Press, Cambridge, 1995
Gromov, M.: Asymptotic Invariants of Infinite Groups, Geometric Group Theory, Vol. 2, Cambridge University Press, Cambridge, 1993.
Gromov, M.: Large Riemannian manifolds, In: Lecture Notes in Math. 1201, Springer, New York, 108–122.
Gromov, M.: Positive curvature, macroscopic dimension, spectral gaps and higher signatures, In: Functional Analysis on the Eve of the 21st Century, Vol. 2, Progr. Math. 132, Birkhäuser, Boston, 1996, pp. 1–213.
Gromov M. (2003). Random walk on random groups, Geom. Funct. Anal. 13(1):73–146
Gromov M. and Lawson H.B. (1983). Positive scalar curvature and the Dirac operator. Publ. I.H.E.S 58:83–196
Ji L. (2004). Asymptotic dimension and the integral K-theoretic Novikov conjecture for arithmetic groups. J. Differential Geom. 69(3):535–544
Keesling J. (1994). The one-dimensional Cech cohomology of the Higson compactification and its corona. Topology Proc 19:129–148
Roe, J.: Coarse cohomology and index theory for complete Riemannian manifolds. Mem. Amer. Math. Soc. 497 (1993)
Roe, J.: Index theory, coarse geometry, and topology of manifolds, CBMS Reg. Conf. Ser. Math. 90, Amer. Math. Soc., Providence, 1996.
Rosenberg J. (1983). C *-algebras, positive scalar curvature, and the Novikov conjecture. Publ. I.H.E.S 58:197–212
Yu G. (1998). The Novikov conjecture for groups with finite asymptotic dimension. Ann. of Math 147(2):325–355
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dranishnikov, A.N. On Hypereuclidean Manifolds. Geom Dedicata 117, 215–231 (2006). https://doi.org/10.1007/s10711-005-9025-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-005-9025-0