On macroscopic dimension of rationally essential manifolds
Geometry & topology, Tome 15 (2011) no. 2, pp. 1107-1124.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We construct a counterexamples in dimensions n > 3 to Gromov’s conjecture that the macroscopic dimension of rationally essential n–dimensional manifolds equals n.

DOI : 10.2140/gt.2011.15.1107
Keywords: macroscopic dimension, essential manifold

Dranishnikov, Alexander 1

1 Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611-8105, USA
@article{GT_2011_15_2_a12,
     author = {Dranishnikov, Alexander},
     title = {On macroscopic dimension of rationally essential manifolds},
     journal = {Geometry & topology},
     pages = {1107--1124},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2011},
     doi = {10.2140/gt.2011.15.1107},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2011.15.1107/}
}
TY  - JOUR
AU  - Dranishnikov, Alexander
TI  - On macroscopic dimension of rationally essential manifolds
JO  - Geometry & topology
PY  - 2011
SP  - 1107
EP  - 1124
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2011.15.1107/
DO  - 10.2140/gt.2011.15.1107
ID  - GT_2011_15_2_a12
ER  - 
%0 Journal Article
%A Dranishnikov, Alexander
%T On macroscopic dimension of rationally essential manifolds
%J Geometry & topology
%D 2011
%P 1107-1124
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2011.15.1107/
%R 10.2140/gt.2011.15.1107
%F GT_2011_15_2_a12
Dranishnikov, Alexander. On macroscopic dimension of rationally essential manifolds. Geometry & topology, Tome 15 (2011) no. 2, pp. 1107-1124. doi : 10.2140/gt.2011.15.1107. http://geodesic.mathdoc.fr/articles/10.2140/gt.2011.15.1107/

[1] G Bell, A Dranishnikov, On asymptotic dimension of groups acting on trees, Geom. Dedicata 103 (2004) 89

[2] J Block, S Weinberger, Aperiodic tilings, positive scalar curvature and amenability of spaces, J. Amer. Math. Soc. 5 (1992) 907

[3] D Bolotov, A Dranishnikov, On Gromov's scalar curvature conjecture, Proc. Amer. Math. Soc. 138 (2010) 1517

[4] K S Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer (1994)

[5] M Brunnbauer, B Hanke, Large and small group homology, J. Topol. 3 (2010) 463

[6] A Dranishnikov, Macroscopic dimension and essential manifolds, to appear, from: "Proceedings of the Conference dedicated to the 75th anniversary of the Steklov Mathematical Institute, Moscow, 2009", Proc. Steklov Inst. Math.

[7] A N Dranishnikov, Y B Rudyak, On the Berstein–Svarc theorem in dimension 2, Math. Proc. Cambridge Philos. Soc. 146 (2009) 407

[8] S M Gersten, Cohomological lower bounds for isoperimetric functions on groups, Topology 37 (1998) 1031

[9] M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1

[10] M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, Vol. 2 (Sussex, 1991)", London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1

[11] M Gromov, Positive curvature, macroscopic dimension, spectral gaps and higher signatures, from: "Functional analysis on the eve of the 21st century, Vol. II (New Brunswick, NJ, 1993)", Progr. Math. 132, Birkhäuser (1996) 1

[12] A S Švarc, The genus of a fibered space, Trudy Moskov. Mat. Obšč. 10 (1961) 217

Cité par Sources :