| Lefschetz Number |
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| CATEGORIES ABOUT LEFSCHETZ FIXED-POINT THEOREM | |
| fixed points | |
| algebraic topology | |
| continuous mappings | |
| mathematical theorems | |
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The counting is subject to some imputed Multiplicity at a fixed point. A weak version of the theorem is enough to show that a mapping without ''any'' fixed point must have rather special topological properties (like a rotation of a circle). For a formal statement, let : be a Continuous Map from a Compact Triangulable Space ''X'' to itself. A point ''x'' of ''X'' is a ''fixed point'' of ''f'' if ''f''(''x'') = ''x''. Denote the Lefschetz number of ''f'' by : By definition this is |
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