منابع مشابه
Every Nontrivial Knot in S Has Nontrivial A-polynomial
We show that every nontrivial knot in the 3-sphere has a nontrivial A-polynomial. In Theorem 1 of [3], Kronheimer and Mrowka give a proof of the following remarkable theorem, thereby establishing the truth of the Property P conjecture. Theorem 0.1 (Kronheimer-Mrowka). Let K be any nontrivial knot in S and let M(r) be the manifold obtained by Dehn surgery on K with slope r with respect to the st...
متن کاملThe Jones Slopes of a Knot
The paper introduces the Slope Conjecture which relates the degree of the Jones polynomial of a knot and its parallels with the slopes of incompressible surfaces in the knot complement. More precisely, we introduce two knot invariants, the Jones slopes (a finite set of rational numbers) and the Jones period (a natural number) of a knot in 3-space. We formulate a number of conjectures for these ...
متن کاملEvery Graph Has an Embedding in S3 Containing No Non-hyperbolic Knot
In contrast with knots, whose properties depend only on their extrinsic topology in S3, there is a rich interplay between the intrinsic structure of a graph and the extrinsic topology of all embeddings of the graph in S3. For example, it was shown by Conway and Gordon that every embedding of the complete graph K7 in S3 contains a non-trivial knot. Later it was shown that for every m ∈ N there i...
متن کاملEvery Graph Has an Embedding in S Containing No Non-hyperbolic Knot
In contrast with knots, whose properties depend only on their extrinsic topology in S3, there is a rich interplay between the intrinsic structure of a graph and the extrinsic topology of all embeddings of the graph in S3. For example, it was shown by Conway and Gordon that every embedding of the complete graph K7 in S3 contains a non-trivial knot. Later it was shown that for every m ∈ N there i...
متن کاملEvery Life Has Equal Value
The 2013 Lasker∼Bloomberg Public Service Award will be given to Bill and Melinda Gates "for leading an historic transformation in the way we view the globe's most pressing health concerns and improving the lives of millions of the world's most vulnerable."
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2018
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-018-1757-x