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Effective topological complexity of orientable-surface groups. (English) Zbl 1498.55002

Summary: We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an orientable surface with respect to its antipodal involution. Our estimates are at most one unit from being optimal, and are closely related to the (regular) topological complexity of non-orientable surfaces.

MSC:

55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20J06 Cohomology of groups
55N25 Homology with local coefficients, equivariant cohomology
68T40 Artificial intelligence for robotics
68Q42 Grammars and rewriting systems
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References:

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