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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)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Whittington, Stuart G. |
| Copyright Year | 2009 |
| Abstract | We consider the number of embeddings of almost unknotted Θk-graphs, 3 ≤ k ≤ 6, in the simple cubic lattice Z3. We show that to exponential order this number is the same as the number of unknotted Θk-graphs. This implies that almost unknotted Θk-graphs are exponentially rare in the set of embeddings of Θk-graphs. We construct almost unknotted surfaces in Z4 by spinning and show that to exponential order the numbers of almost unknotted spun Θk are equal to the numbers of unknotted spun Θk, 4 ≤ k ≤ 6. The case of k = 3 is open. |
| Starting Page | 11 |
| Ending Page | 15 |
| Page Count | 5 |
| File Format | PDF HTM / HTML |
| Volume Number | 92 |
| Alternate Webpage(s) | https://sites.chem.utoronto.ca/chemistry/swhittin/kyoto-whittington.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
