Almost unknotted embeddings of graphs and surfaces (結び目とソフトマター物理学--高分子のトポロジー、そして物理学、数学および生物学における関連する話題)

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概要

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• We consider the number of embeddings of almost unknotted Θ_k-graphs, 3≤k≤6, in the simple cubic lattice Z^3. We show that to exponential order this number is the same as the number of unknotted Θ_k-graphs. This implies that almost unknotted Θ_k-graphs are exponentially rare in the set of embeddings of Θ_k-graphs. We construct almost unknotted surfaces in Z^4 by spinning and show that to exponential order the numbers of almost unknotted spun Θ_k are equal to the numbers of unknotted spun Θ_k, 4≤k≤6. The case of k=3 is open.

• 2009-04-20

著者

• Whittington S.G.

  University of Toronto

関連論文

• Almost unknotted embeddings of graphs and surfaces (結び目とソフトマター物理学--高分子のトポロジー、そして物理学、数学および生物学における関連する話題)

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