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THE GENERALIZED DEHN TWIST ALONG A FIGURE EIGHT

    https://doi.org/10.1142/S1793525313500155Cited by:1 (Source: Crossref)

    For any unoriented loop on a compact connected oriented surface with one boundary component, we introduce a generalized Dehn twist along the loop as a certain automorphism of the completed group ring of the fundamental group of the surface. If the loop is simple, this corresponds to the right-handed Dehn twist, and in particular is realized as a diffeomorphism of the surface. We investigate the case where the loop has a single transverse double point, and show that in this case the generalized Dehn twist is not realized as a diffeomorphism.

    AMSC: 57N05, 20F34