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Framed Stratified Sets in Morse Theory
Published online by Cambridge University Press: 20 November 2018
Abstract
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. We then apply these ideas to Morse theory, in order to generalize results of Franks and Iriye-Kono.
More precisely, consider a Morse function $f$ on a closed manifold $M$. We investigate the relations between the attaching maps in a $\text{CW}$ complex determined by $f$, and the moduli spaces of gradient flow lines of $f$, with respect to some Riemannian metric on $M$.
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- Copyright © Canadian Mathematical Society 2002