A combinatorial Lefschetz fixed point formula |
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Authors: | Neeta Pandey |
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Affiliation: | (1) Stat.-Math. Unit, Indian Statistical Institute, 203 BT Road, 700035 Calcutta, India |
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Abstract: | We define a class of simplicial maps — those which are “expanding directions preserving” — from a barycentric subdivision to the original simplicial complex. These maps naturally induce a self map on the links of their fixed points. The local index at a fixed point of such a map turns out to be the Lefschetz number of the induced map on the link of the fixed point in relative homology. We also show that a weakly hyperbolic [4] simplicial map sdnK →K is expanding directions preserving. |
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Keywords: | Lefschetz fixed point formula fixed point indices simplicial complexes |
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