Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
We exhibit geometric situations where higher indices of the spinor Dirac operator on a spin manifold N are obstructions to positive scalar curvature on an ambient manifold M that contains N as a submanifold. In the main result of this note, we show that the Rosenberg index of N is an obstruction to positive scalar curvature on M if N↪M ↠ B is a fiber bundle of spin manifolds with B aspherical and π1(B) of finite asymptotic dimension. The proof is based on a new variant of the multipartitioned manifold index theorem which might be of independent interest. Moreover, we present an analogous statement for codimension-one submanifolds. We also discuss some elementary obstructions using the Â-genus of certain submanifolds.
Keywords: positive scalar curvature, multipartitioned manifolds, coarse index theory, asymptotic dimension, aspherical manifolds
Zeidler, Rudolf 1
@article{10_2140_agt_2017_17_3081,
author = {Zeidler, Rudolf},
title = {An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds},
journal = {Algebraic and Geometric Topology},
pages = {3081--3094},
publisher = {mathdoc},
volume = {17},
number = {5},
year = {2017},
doi = {10.2140/agt.2017.17.3081},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3081/}
}
TY - JOUR AU - Zeidler, Rudolf TI - An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds JO - Algebraic and Geometric Topology PY - 2017 SP - 3081 EP - 3094 VL - 17 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3081/ DO - 10.2140/agt.2017.17.3081 ID - 10_2140_agt_2017_17_3081 ER -
%0 Journal Article %A Zeidler, Rudolf %T An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds %J Algebraic and Geometric Topology %D 2017 %P 3081-3094 %V 17 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.3081/ %R 10.2140/agt.2017.17.3081 %F 10_2140_agt_2017_17_3081
Zeidler, Rudolf. An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds. Algebraic and Geometric Topology, Tome 17 (2017) no. 5, pp. 3081-3094. doi: 10.2140/agt.2017.17.3081
Cité par Sources :