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We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements in higher homotopy and homology groups of these spaces, which, in contrast to previous approaches, are of infinite order and survive in the (observer) moduli space of such metrics.
Along the way we construct smooth fiber bundles over spheres whose total spaces have non-vanishing -genera, thus establishing the non-multiplicativity of the -genus in fiber bundles with simply connected base.
Hanke, Bernhard 1 ; Schick, Thomas 2 ; Steimle, Wolfgang 3
@article{PMIHES_2014__120__335_0,
author = {Hanke, Bernhard and Schick, Thomas and Steimle, Wolfgang},
title = {The space of metrics of positive scalar curvature},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {335--367},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {120},
year = {2014},
doi = {10.1007/s10240-014-0062-9},
zbl = {1321.58008},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-014-0062-9/}
}
TY - JOUR AU - Hanke, Bernhard AU - Schick, Thomas AU - Steimle, Wolfgang TI - The space of metrics of positive scalar curvature JO - Publications Mathématiques de l'IHÉS PY - 2014 SP - 335 EP - 367 VL - 120 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-014-0062-9/ DO - 10.1007/s10240-014-0062-9 LA - en ID - PMIHES_2014__120__335_0 ER -
%0 Journal Article %A Hanke, Bernhard %A Schick, Thomas %A Steimle, Wolfgang %T The space of metrics of positive scalar curvature %J Publications Mathématiques de l'IHÉS %D 2014 %P 335-367 %V 120 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-014-0062-9/ %R 10.1007/s10240-014-0062-9 %G en %F PMIHES_2014__120__335_0
Hanke, Bernhard; Schick, Thomas; Steimle, Wolfgang. The space of metrics of positive scalar curvature. Publications Mathématiques de l'IHÉS, Tome 120 (2014), pp. 335-367. doi: 10.1007/s10240-014-0062-9
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