Geometric Bordisms of the Accola-Maclachlan, Kulkarni and Wiman Type II Surfaces

2023/12/04 by Ferrari, Leonardo
#14H37 (Secondary) #30F10 (Primary) #57R40 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2312.01821

Abstract

In this paper, we prove that the Accola-Maclachlan surface of genus g bounds geometrically an orientable compact hyperbolic 3-manifold for every genus. For infinitely many genera, this is an explicit example of non-arithmetic surface that bounds geometrically a non-arithmetic manifold. We also provide explicit geodesic embeddings to the Wiman type II and Kulkarni surfaces of every genus, and prove that these surfaces bound geometrically a compact, orientable manifold for g≡ 1 ( mod 2) or g ≡ 3 ( mod 8), respectively.

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