Acta Applicandae Mathematica

, Volume 67, Issue 3, pp 225–235

Size Functions from a Categorical Viewpoint

  • Francesca Cagliari
  • Massimo Ferri
  • Paola Pozzi
Article

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

Abstract

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

Authors and Affiliations

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