ON POSITIVELY CURVED FOUR-MANIFOLDS WITH S(1)-SYMMETRY

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It is well known by the work of Hsiang and Kleiner that every closed oriented positively curved four-dimensional manifold with an effective isometric S-1-action is homeomorphic to S-4 or CP2. As stated, it is a topological classification. The primary goal of this paper is to show that it is indeed a diffeomorphism classification for such four-dimensional manifolds. The proof of this diffeomorphism classification also shows an even stronger statement that every positively curved simply connected four-manifold with an isometric circle action admits another smooth circle action which extends to a two-dimensional torus action and is equivariantly diffeomorphic to a linear action on S-4 or CP2. The main strategy is to analyze all possible topological configurations of effective circle actions on simply connected four-manifolds by using the so-called replacement trick of Pao.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2011-07
Language
English
Article Type
Article
Keywords

CIRCLE ACTIONS; MANIFOLDS; SYMMETRY; CURVATURE; TOPOLOGY; TORUS

Citation

INTERNATIONAL JOURNAL OF MATHEMATICS, v.22, no.7, pp.981 - 990

ISSN
0129-167X
URI
http://hdl.handle.net/10203/98420
Appears in Collection
MA-Journal Papers(저널논문)
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