Acta Applicandae Mathematica

, Volume 67, Issue 3, pp 225–235

Size Functions from a Categorical Viewpoint

  • Francesca Cagliari
  • Massimo Ferri
  • Paola Pozzi


A new categorical approach to size functions is given. Using this point of view, it is shown that size functions of a Morse map, f: M→ℜ can be computed through the 0-dimensional homology. This result is extended to the homology of arbitrary degree in order to obtain new invariants of the shape of the graph of the given map.

size function size functor Morse function critical point 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Francesca Cagliari
    • 1
  • Massimo Ferri
    • 1
  • Paola Pozzi
    • 1
  1. 1.Dipartimento di MatematicaUniversitàBolognaItaly

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