Every genus one algebraically slice knot is 1-solvable
نویسندگان
چکیده
منابع مشابه
Solvable Points on Genus One Curves
A genus one curve defined over Q which has points over Qp for all primes p may not have a rational point. It is natural to study the classes of Q-extensions over which all such curves obtain a global point. In this article, we show that every such genus one curve with semistable Jacobian has a point defined over a solvable extension of Q.
متن کاملOrder 2 Algebraically Slice Knots
The concordance group of algebraically slice knots is the subgroup of the classical knot concordance group formed by algebraically slice knots. Results of Casson and Gordon and of Jiang showed that this group contains in infinitely generated free (abelian) subgroup. Here it is shown that the concordance group of algebraically slice knots also contain elements of finite order; in fact it contain...
متن کاملReasoning Algebraically About P-Solvable Loops
We present a method for generating polynomial invariants for a subfamily of imperative loops operating on numbers, called the P-solvable loops. The method uses algorithmic combinatorics and algebraic techniques. The approach is shown to be complete for some special cases. By completeness we mean that it generates a set of polynomial invariants from which, under additional assumptions, any polyn...
متن کامل3-MANIFOLD KNOT GENUS is NP-complete
One of the central questions in topology is determining whether a given curve is knotted or unknotted. An algorithm to decide this question was given by Haken in 1961, using the technique of normal surfaces. These surfaces are rigid, discretized surfaces, well suited for algorithmic analysis. Any oriented surface without boundary can be obtained from a sphere by adding “handles”. The number of ...
متن کاملSolvable Points on Genus One Curves over Local Fields
Let F be a field complete with respect to a discrete valuation whose residue field is perfect of characteristic p > 0. We prove that every smooth, projective, geometrically irreducible curve of genus one defined over F with a non-zero divisor of degree a power of p has a solvable point over F .
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: Transactions of the American Mathematical Society
سال: 2019
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7682