Acta Applicandae Mathematica

, Volume 67, Issue 3, pp 225–235

Size Functions from a Categorical Viewpoint


  • Francesca Cagliari
    • Dipartimento di MatematicaUniversità
  • Massimo Ferri
    • Dipartimento di MatematicaUniversità
  • Paola Pozzi
    • Dipartimento di MatematicaUniversità

DOI: 10.1023/A:1011923819754

Cite this article as:
Cagliari, F., Ferri, M. & Pozzi, P. Acta Applicandae Mathematicae (2001) 67: 225. doi:10.1023/A:1011923819754


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 functionsize functorMorse functioncritical point

Copyright information

© Kluwer Academic Publishers 2001