2016/12/08 by Donald M. Davis, Davis, Donald M.
Computer Science · Mathematics · #55M30 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #msc:55M30
paper · pdf · doi:10.48550/arxiv.1612.02747
Corrected a mistake in the most recent version
openalex publication_date 2016/12/08 · arxiv created 2017/02/02 · arxiv updated 2017/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Cohen and Vandembroucq proved that the reduced topological complexity of the Klein bottle is 4. Simultaneously and independently, we announced a proof of the same result. Mistakes were found in our argument, which was quite different than theirs. After correcting these, we found that our description of the obstruction class agreed with theirs. Our approach to showing that this obstruction is nonzero failed to do so, while theirs did not fail. Here we discuss our approach, which deals more directly with the simplicial structure of the Klein bottle.