caa a22 4500 445862467 CHVBK 20180317145447.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00031-011-9154-5 doi (NATIONALLICENCE)springer-10.1007/s00031-011-9154-5 Torsion in equivariant cohomology and Cohen-Macaulay G -actions [Elektronische Daten] [Oliver Goertsches, Sönke Rollenske] We show that the well-known fact that the equivariant cohomology (with real coefficients) of a torus action is a torsion-free module if and only if the map induced by the inclusion of the fixed point set is injective generalises to actions of arbitrary compact connected Lie groups if one replaces the fixed point set by the set of points with isotropy rank equal to the rank of the acting group. This is true essentially because the action on this set is always equivariantly formal. In case this set is empty we show that the induced action on the set of points with highest occuring isotropy rank is Cohen-Macaulay. It turns out that just as equivariant formality of an action is equivalent to equivariant formality of the action of a maximal torus, the same holds true for equivariant injectivity and the Cohen-Macaulay property. In addition, we find a topological criterion for equivariant injectivity in terms of orbit spaces. Springer Science+Business Media, LLC, 2011 Goertsches Oliver Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Köln, Germany aut Rollenske Sönke Institut für Mathematik, Joh. Gutenberg-Universität Mainz, 55099, Mainz, Germany aut Transformation Groups SP Birkhäuser Verlag Boston 16/4(2011-12-01), 1063-1080 1083-4362 16:4<1063 2011 16 31 https://doi.org/10.1007/s00031-011-9154-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-011-9154-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goertsches Oliver Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Köln, Germany aut NATIONALLICENCE 700 1- Rollenske Sönke Institut für Mathematik, Joh. Gutenberg-Universität Mainz, 55099, Mainz, Germany aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/4(2011-12-01), 1063-1080 1083-4362 16:4<1063 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer