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Framed Stratified Sets in Morse Theory

Open Access article
 Printed: Apr 2002
  • AndrĂ© Lebel
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In this paper, we present a smooth framework for some aspects of the ``geometry of CW complexes'', in the sense of Buoncristiano, Rourke and Sanderson \cite{[BRS]}. We then apply these ideas to Morse theory, in order to generalize results of Franks \cite{[F]} and Iriye-Kono \cite{[IK]}. More precisely, consider a Morse function $f$ on a closed manifold $M$. We investigate the relations between the attaching maps in a CW complex determined by $f$, and the moduli spaces of gradient flow lines of $f$, with respect to some Riemannian metric on~$M$.
MSC Classifications: 57R70, 57N80, 55N45 show english descriptions Critical points and critical submanifolds
Products and intersections
57R70 - Critical points and critical submanifolds
57N80 - Stratifications
55N45 - Products and intersections

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