2020/03/26 by Yi Ni, Chao Wang, Ni, Yi +3
Mathematics · #57M60 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M60
paper · pdf · doi:10.48550/arxiv.2003.11773
17 pages, 5 figures
arxiv created 2020/03/26 · openalex publication_date 2020/03/26 · arxiv updated 2020/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite group acting on a connected compact surface Σ, and M be an integer homology 3-sphere. We show that if each element of G is extendable over M with respect to a fixed embedding Σ→ M, then G is extendable over some M' which is 1-dominated by M. From this result, in the orientable category we classify all periodic automorphisms of closed surfaces that are extendable over the 3-sphere. The corresponding embedded surface of such an automorphism can always be a Heegaard surface.