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arxiv: 1710.04711 · v2 · pith:3R7LSYWVnew · submitted 2017-10-12 · 🧮 math.AT · math.GT

The topological complexity of the free product

classification 🧮 math.AT math.GT
keywords complexityfreeproducttopologicalcohomologicaldimensiondiscreteformula
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We prove the formula $TC(G\ast H)=\max\{TC(G), TC(H), cd(G\times H)\}$ for the topological complexity of the free product of discrete groups with cohomological dimension >2.

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    Develops practical tools for configuration sets F(G,k) in groups and applies them to homogeneous linear systems in finite fields and connectivity of Cayley graphs Cay(G^k, F(G,k)).