Effective topological complexity of orientable-surface groups

2019/07/24 by Natalia Cadavid-Aguilar, Cadavid-Aguilar, Natalia, Jesús González +1
Mathematics · #20F10 #20J06 #55M30. 55N25 #68Q42 #68T40 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:20F10 #msc:20J06 #msc:55M30. #msc:55N25 #msc:68Q42 #msc:68T40

paper · pdf · doi:10.48550/arxiv.1907.10212

27 pages. This new version of the paper includes a detailed application of the cohomology calculations to the effective topological complexity of oriented surfaces

arxiv created 2020/03/03 · arxiv updated 2020/03/04

Abstract

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.

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