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Abstract: The main result of this note is a parametrized version of the Borsuk-Ulamtheorem. We show that for a continuous family of Borsuk-Ulam situations,parameterized by points of a compact manifold W, its solution set also dependscontinuously on the parameter space W. Continuity here means that the solutionset supports a homology class which maps onto the fundamental class of W. WhenW is a subset of Euclidean space, we also show how to construct such acontinuous family starting from a family depending in the same way continuouslyon the points of the boundary of W. This solves a problem related to aconjecture which is relevant for the construction of equilibrium strategies inrepeated two-player games with incomplete information. A new method ofindependent interest used in this context is a canonical symmetric squaringconstruction in Cech homology with coefficients in Z-2Z.



Author: Thomas Schick Georg-August Universität Göttingen, Robert Simon London School of Economics, Stanislav Spiez Polish Academy of Sc

Source: https://arxiv.org/



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