Geodesic
Classification of prime 3-manifolds with $\sigma$-invariant greater than $\Bbb{RP}^3$
Hubert L. Bray1 ; André Neves2
1 Department of Mathematics, Columbia University, New York, NY 10027, United States
2 Instituto Superior Tećnico, Lisbon, Portugal and Department of Mathematics, Stanford Universit, Stanford, CA 94305, United States
Annals of mathematics, Tome 159 (2004) no. 1, pp. 407-424.

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

In this paper we compute the $\sigma$-invariants (sometimes also called the smooth Yamabe invariants) of $\mathbb{RP}^3$ and $\mathbb{RP}^2 \times S^1$ (which are equal) and show that the only prime $3$-manifolds with larger $\sigma$-invariants are $S^3$, $S^2 \times S^1$, and $S^2 \tilde\times S^1$ (the nonorientable $S^2$ bundle over $S^1$). More generally, we show that any $3$-manifold with $\sigma$-invariant greater than $\mathbb{RP}^3$ is either $S^3$, a connect sum with an $S^2$ bundle over $S^1$, or has more than one nonorientable prime component. A corollary is the Poincaré conjecture for $3$-manifolds with $\sigma$-invariant greater than $\mathbb{RP}^3$.
DOI : 10.4007/annals.2004.159.407

Hubert L. Bray 1 ; André Neves 2

1 Department of Mathematics, Columbia University, New York, NY 10027, United States
2 Instituto Superior Tećnico, Lisbon, Portugal and Department of Mathematics, Stanford Universit, Stanford, CA 94305, United States 
@article{10_4007_annals_2004_159_407,
     author = {Hubert L. Bray and Andr\'e Neves},
     title = {Classification of prime 3-manifolds with $\sigma$-invariant greater than $\Bbb{RP}^3$},
     journal = {Annals of mathematics},
     pages = {407--424},
     publisher = {mathdoc},
     volume = {159},
     number = {1},
     year = {2004},
     doi = {10.4007/annals.2004.159.407},
     mrnumber = {2052359},
     zbl = {1066.53077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2004.159.407/}
}
TY  - JOUR
AU  - Hubert L. Bray
AU  - André Neves
TI  - Classification of prime 3-manifolds with $\sigma$-invariant greater than $\Bbb{RP}^3$
JO  - Annals of mathematics
PY  - 2004
SP  - 407
EP  - 424
VL  - 159
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2004.159.407/
DO  - 10.4007/annals.2004.159.407
LA  - en
ID  - 10_4007_annals_2004_159_407
ER  - 
%0 Journal Article
%A Hubert L. Bray
%A André Neves
%T Classification of prime 3-manifolds with $\sigma$-invariant greater than $\Bbb{RP}^3$
%J Annals of mathematics
%D 2004
%P 407-424
%V 159
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2004.159.407/
%R 10.4007/annals.2004.159.407
%G en
%F 10_4007_annals_2004_159_407
Hubert L. Bray; André Neves. Classification of prime 3-manifolds with $\sigma$-invariant greater than $\Bbb{RP}^3$. Annals of mathematics, Tome 159 (2004) no. 1, pp. 407-424. doi : 10.4007/annals.2004.159.407. http://geodesic.mathdoc.fr/articles/10.4007/annals.2004.159.407/

Cité par Sources :