, Volume 67, Issue 3, pp 225-235

Size Functions from a Categorical Viewpoint

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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.