Petrie conjecture
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1 Introduction
The Petrie conjecture was formulate in the following context: suppose that a Lie group acts on a closed smooth manifold , what constraints does this place on the topology of in general and on the Pontrjagin classes of in particular.
Petrie restricted his attention to actions of the Lie group on manifolds which are homotopy equivalent to . He formulate the following
Conjecture 0.1 [Petrie1972]. Suppose that is a closed smooth manifold homotopy equivalent to and that acts effectively on . Then the total Pontrjagin class of agrees 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