Petrie conjecture
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Revision as of 10:49, 27 November 2010
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1 Introduction
Tex syntax error, what constraints does this place on the topology of
Tex syntax errorin general and on the Pontrjagin classes of
Tex syntax errorin particular. Petrie restricted his attention to actions of the Lie group on manifolds
Tex syntax errorwhich are homotopy equivalent to . He formulated the following
Conjecture 0.1 [Petrie1972].
Suppose thatTex syntax erroris a closed smooth manifold homotopy equivalent to and that acts effectively on
Tex syntax error. Then the total Pontrjagin class of
Tex syntax erroragrees with that of .
2 References
- [Petrie1972] T. Petrie, Smooth -actions on homotopy complex projective spaces and related topics, Bull. Amer. Math. Soc. 78 (1972), 105–153. MR0296970 Zbl 0247.57010