A constructive proof of Ky Fan's generalization of Tucker's lemma |
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| Authors: | Timothy Prescott Francis Edward Su |
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| Institution: | a Department of Mathematics, University of California, Los Angeles, CA 90095, USA
b Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA |
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| Abstract: | We present a proof of Ky Fan's combinatorial lemma on labellings of triangulated spheres that differs from earlier proofs in that it is constructive. We slightly generalize the hypotheses of Fan's lemma to allow for triangulations of Sn that contain a flag of hemispheres. As a consequence, we can obtain a constructive proof of Tucker's lemma that holds for a more general class of triangulations than the usual version. |
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| Keywords: | primary 55M20 secondary 05A99 52B70 |
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