126.完全2部グラフK_<4,4>の最小シート数本表現について

概要

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In this paper we investigate the book presentation of K_<4,4> with the minimum number of sheet and decide the topological symmetry group of such spatial K_<4,4>. Let ⊿ be a Hamilton path of K_<4,4> and ψ: (K_<4,4>, ⊿)→(ℬ_n, Ξ) be a book presentation with respect to ⊿ i.e. ψ is an embedding with ψ (⊿)⊂Ξ and ψ (e) is contained in a sheet S_i for any edge e of K_<4,4>. Then the minimum number of sheets is 4 and there are 3 types, TSG (K^<(i)>_<4 4>), (i=1, 2, 3), of presentation of K_<4,4> with 4 sheets up to homeomorphism of R^3. Let TSG (K^<(i)>_<4 4>) be the topological symmetry group of K^<(i)>_<4 4> i.e. TSG(^<(i)>_<4 4>)={σ∈Aut(K_<4,4>)| ∃ homeomorphism f: R^3→R^3 with ψ_iσ=fψ_i: where ψ_i: K_<4,4>→R^3 is an embedding with ψ_i (K_<4,4>)=K^<(i)>_<4,4>}. And we can decide TSG (K^<(i)>_<4,4>), (i=1, 2, 3) of such 3 types of spatial K_<4,4>. TSG (K^<(1)>_<4,4>)≅<(15), (37), (1357), (26, (48), (2468), (12...8)>⊂S_2[S_4] TSG (K^<(2)>_<4,4>)≅D_8 and TSG (K^<(3)>_<4,4>)≌D_4 The key points to decide TSG (K^<(i)>_<4,4>) are the list of knots and links contained in the spatial K^<(i)>_<4,4>, (i=1, 2, 3).
東京女子大学の論文
1998-03-09