Torsion in equivariant cohomology and Cohen-Macaulay G -actions
Identifieur interne : 000244 ( Main/Exploration ); précédent : 000243; suivant : 000245Torsion in equivariant cohomology and Cohen-Macaulay G -actions
Auteurs : Oliver Goertsches [Allemagne] ; Sönke Rollenske [Allemagne]Source :
- Transformation Groups [ 1083-4362 ] ; 2011-12-01.
Abstract
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.
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DOI: 10.1007/s00031-011-9154-5
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Gutenberg-Universität Mainz, 55099, Mainz</wicri:regionArea><wicri:noRegion>55099, Mainz</wicri:noRegion><wicri:noRegion>Mainz</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Allemagne</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Transformation Groups</title><title level="j" type="abbrev">Transformation Groups</title><idno type="ISSN">1083-4362</idno><idno type="eISSN">1531-586X</idno><imprint><publisher>SP Birkhäuser Verlag Boston</publisher><pubPlace>Boston</pubPlace><date type="published" when="2011-12-01">2011-12-01</date><biblScope unit="volume">16</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="1063">1063</biblScope><biblScope unit="page" to="1080">1080</biblScope></imprint><idno type="ISSN">1083-4362</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1083-4362</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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.</div></front></TEI><affiliations><list><country><li>Allemagne</li></country><region><li>District de Cologne</li><li>Rhénanie-du-Nord-Westphalie</li></region><settlement><li>Cologne</li></settlement><orgName><li>Université de Cologne</li></orgName></list><tree><country name="Allemagne"><region name="Rhénanie-du-Nord-Westphalie"><name sortKey="Goertsches, Oliver" sort="Goertsches, Oliver" uniqKey="Goertsches O" first="Oliver" last="Goertsches">Oliver Goertsches</name></region><name sortKey="Goertsches, Oliver" sort="Goertsches, Oliver" uniqKey="Goertsches O" first="Oliver" last="Goertsches">Oliver Goertsches</name><name sortKey="Rollenske, Sonke" sort="Rollenske, Sonke" uniqKey="Rollenske S" first="Sönke" last="Rollenske">Sönke Rollenske</name><name sortKey="Rollenske, Sonke" sort="Rollenske, Sonke" uniqKey="Rollenske S" first="Sönke" last="Rollenske">Sönke Rollenske</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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