Let be a finite complex, let be a continuous map. If , then has a fixed point.

Munkres, J. R. "Application: The Lefschetz Fixed-Point Theorem." §22 in Elements of Algebraic Topology. New York: Perseus Books Pub.,pp. 121-128, 1993.

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Weisstein, Eric W. "Lefshetz Fixed Point Formula." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LefshetzFixedPointFormula.html