@conference {13275,
	title = {Cancellation of critical points in 2D and 3D Morse and Morse-Smale complexes},
	booktitle = {Discrete Geometry for Computer Imagery},
	year = {2008},
	month = {2008///},
	pages = {117 - 128},
	abstract = {Morse theory studies the relationship between the topology of a manifold M and the critical points of a scalar function f defined on M. The Morse-Smale complex associated with f induces a subdivision of M into regions of uniform gradient flow, and represents the topology of M in a compact way. Function f can be simplified by cancelling its critical points in pairs, thus simplifying the topological representation of M, provided by the Morse-Smale complex. Here, we investigate the effect of the cancellation of critical points of f in Morse-Smale complexes in two and three dimensions by showing how the change of connectivity of a Morse-Smale complex induced by a cancellation can be interpreted and understood in a more intuitive and straightforward way as a change of connectivity in the corresponding ascending and descending Morse complexes. We consider a discrete counterpart of the Morse-Smale complex, called a quasi-Morse complex, and we present a compact graph-based representation of such complex and of its associated discrete Morse complexes, showing also how such representation is affected by a cancellation.},
	doi = {10.1007/978-3-540-79126-3_12},
	author = {{\v C}omi{\'c},L. and De Floriani, Leila}
}
