Geodesic
Large Riemannian manifolds which are flexible
Alexander N. Dranishnikov1 ; Steven C. Ferry2 ; Shmuel Weinberger3
1 Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, United States
2 Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, United States
3 Department of Mathematics, University of Chicago, Chicago, IL 60637-1514, United States
Annals of mathematics, Tome 157 (2003) no. 3, pp. 919-938.

Voir la notice de l'article provenant de la source Annals of Mathematics website

For each $k \in \mathbb{Z}$, we construct a uniformly contractible metric on Euclidean space which is not mod $k$ hypereuclidean. We also construct a pair of uniformly contractible Riemannian metrics on $\mathbb{R}^n$, $n \ge 11$, so that the resulting manifolds $Z$ and $Z’$ are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism. We show that for these spaces the $C^*$-algebra assembly map $K_*^{lf}(Z) \to K_*(C^*(Z))$ from locally finite $K$-homology to the $K$-theory of the bounded propagation algebra is not a monomorphism. This shows that an integral version of the coarse Novikov conjecture fails for real operator algebras. If we allow a single cone-like singularity, a similar construction yields a counterexample for complex $C^*$-algebras.
DOI : 10.4007/annals.2003.157.919

Alexander N. Dranishnikov 1 ; Steven C. Ferry 2 ; Shmuel Weinberger 3

1 Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, United States
2 Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, United States
3 Department of Mathematics, University of Chicago, Chicago, IL 60637-1514, United States 
@article{10_4007_annals_2003_157_919,
     author = {Alexander N. Dranishnikov and Steven C. Ferry and Shmuel Weinberger},
     title = {Large {Riemannian} manifolds which are flexible},
     journal = {Annals of mathematics},
     pages = {919--938},
     publisher = {mathdoc},
     volume = {157},
     number = {3},
     year = {2003},
     doi = {10.4007/annals.2003.157.919},
     mrnumber = {1983785},
     zbl = {1051.53035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.919/}
}
TY  - JOUR
AU  - Alexander N. Dranishnikov
AU  - Steven C. Ferry
AU  - Shmuel Weinberger
TI  - Large Riemannian manifolds which are flexible
JO  - Annals of mathematics
PY  - 2003
SP  - 919
EP  - 938
VL  - 157
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.919/
DO  - 10.4007/annals.2003.157.919
LA  - en
ID  - 10_4007_annals_2003_157_919
ER  - 
%0 Journal Article
%A Alexander N. Dranishnikov
%A Steven C. Ferry
%A Shmuel Weinberger
%T Large Riemannian manifolds which are flexible
%J Annals of mathematics
%D 2003
%P 919-938
%V 157
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.919/
%R 10.4007/annals.2003.157.919
%G en
%F 10_4007_annals_2003_157_919
Alexander N. Dranishnikov; Steven C. Ferry; Shmuel Weinberger. Large Riemannian manifolds which are flexible. Annals of mathematics, Tome 157 (2003) no. 3, pp. 919-938. doi : 10.4007/annals.2003.157.919. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.919/

Cité par Sources :