We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Framed Knots.
- Authors
Elhamdadi, Mohamed; Hajij, Mustafa; Istvan, Kyle
- Abstract
Note that by Proposition 9 above, HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>D</mi><mn>1</mn></msub></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>D</mi><mn>2</mn></msub></math> ht have the same writhe. Suppose that HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mn>1</mn></msub></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mn>2</mn></msub></math> ht are embeddings. However, this definition is more involved when the torus HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>T</mi><mn>2</mn></msup></math> ht is embedded in HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>S</mi><mn>3</mn></msup></math> ht . The decision to construct HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi> </mi><mi mathvariant="bold">W</mi></msub></math> ht by proceeding backward along the knot is made to ensure consistency with other characterizations of the framing integer given in this text, such as the self-linking number. We could alternatively have defined the map HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi> </mi><mi mathvariant="bold">W</mi></msub></math> ht by proceeding forward along the knot and negating the value I m i .
- Subjects
KNOT theory; INTERSECTION numbers; VON Neumann algebras
- Publication
Mathematical Intelligencer, 2020, Vol 42, Issue 4, p7
- ISSN
0343-6993
- Publication type
Article
- DOI
10.1007/s00283-020-09990-0