The Morse-Bott inequalities, orientations, and the Thom isomorphism in   Morse homology
  The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities are sometimes stated under incorrect orientation assumptions. We show that these assumptions are insufficient with an explicit counterexample and clarify the origin of the mistake. 
Thomas O. Rot
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