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Goertsches, Oliver and Rollenske, Soenke (2011). Torsion in equivariant cohomology and Cohen-Macaulay G-actions. Transform. Groups, 16 (4). S. 1063 - 1081. NEW YORK: SPRINGER BIRKHAUSER. ISSN 1531-586X

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Abstract

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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Goertsches, Oliver UNSPECIFIED UNSPECIFIED UNSPECIFIED Rollenske, Soenke UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-485061
DOI:	10.1007/s00031-011-9154-5
Journal or Publication Title:	Transform. Groups
Volume:	16
Number:	4
Page Range:	S. 1063 - 1081
Date:	2011
Publisher:	SPRINGER BIRKHAUSER
Place of Publication:	NEW YORK
ISSN:	1531-586X
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/48506