Cancellation of Critical Points in 2D and 3D Morse and Morse-Smale Complexes

  • Lidija Čomić
  • Leila De Floriani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)

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.

Keywords

Cell Complex Morse Theory Morse Function Integral Line Dual Complex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Lidija Čomić
    • 1
  • Leila De Floriani
    • 2
  1. 1.FTNUniversity of Novi Sad(Serbia)
  2. 2.University of Genova (Italy) and University of Maryland(USA)

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