In mathematics, the Milnor conjecture was a proposal by John Milnor (1970) of a description of the Milnor K-theory (mod 2) of a general field F with characteristic...

Milnor conjecture may refer to: Milnor conjecture (K-theory) in algebraic K-theory Milnor conjecture (knot theory) in knot theory Milnor conjecture (Ricci...

mathematics, Milnor K-theory is an algebraic invariant (denoted K ∗ ( F ) {\displaystyle K_{*}(F)} for a field F {\displaystyle F} ) defined by John Milnor (1970)...

Milnor K-theory modulo 2 is the Milnor conjecture, proven by Vladimir Voevodsky. The analogous statement for odd primes is the Bloch-Kato conjecture,...

Milnor conjecture (Vladimir Voevodsky, 2003) Kirillov's conjecture (Ehud Baruch, 2003) Kouchnirenko's conjecture (Bertrand Haas, 2002) n! conjecture (Mark...

quadratic L-group L 4 k + 2 {\displaystyle L_{4k+2}} , and thus analogous to the other invariants from L-theory: the signature, a 4 k {\displaystyle 4k}...

Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965...

norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively elementary formulation...

conjecture of K-theory, extending the Milnor conjecture, a proof of which was announced in 2009). They are also called the Tamagawa number conjecture...

characteristic 0. There is a conjecture named the Deligne–Milnor conjecture for the differential interpretation of a formula of Milnor for Milnor fibres, as part of...

described separately in the paper (Kervaire & Milnor 1963), which was influential in the development of surgery theory. In fact, these calculations can be formulated...

proof of the Milnor conjecture and motivic Bloch–Kato conjectures and for the univalent foundations of mathematics and homotopy type theory. Vladimir Voevodsky's...

John Milnor: Barratt–Milnor sphere Fáry–Milnor theorem Milnor conjecture in algebraic K-theory Milnor conjecture in knot theory Milnor conjecture concerning...

surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by John Milnor (1961)...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

Chan lists Legendre's conjecture as "Sierpinski's Postulate". Ribenboim 2004, Prime ⁠ k {\displaystyle k} ⁠-tuples conjecture, pp. 201–202. Sandifer...

ISBN 978-0-387-94426-5. Sullivan, Dennis (July 1974). "Genetics of homotopy theory and the Adams conjecture" (PDF). Annals of Mathematics. 2. 100 (1): 1–79. doi:10.2307/1970841...

\mathbf {Z} (j)),} where KjM(k) is the jth Milnor K-group of k. Since Milnor K-theory of a field is defined explicitly by generators and relations, this...

proving the (motivic) Bloch–Kato conjecture (2009). It is a generalization of the Milnor conjecture of algebraic K-theory, which was proved by Voevodsky...

This conjecture is true in dimensions 1, 2, and 3, by the above classification results, but is known to be false in dimension 7 due to the Milnor spheres...

uses algebraic K-theory, and appropriate Milnor K-groups generalize the K 1 {\displaystyle K_{1}} used in one-dimensional class field theory. Frobenioid...

In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by...

category of mixed motives and the proof of the Milnor and Bloch-Kato conjectures. A1 homotopy theory is founded on a category called the A1 homotopy...

applications. Vladimir Voevodsky's Fields Medal-winning proof of the Milnor conjecture uses these motives as a key ingredient. There are different definitions...

it's known as the generalized Chern conjecture for manifolds that are locally a product of surfaces. J. Milnor, On the existence of a connection with...

In knot theory, an area of mathematics, the link group of a link is an analog of the knot group of a knot. They were described by John Milnor in his Ph...

as noticed by John Milnor in 1955 (written down by Shiing-Shen Chern in 1955.). For manifolds of dimension 6 or higher the conjecture is open. An example...

given by the length of the minimal path between the elements. A theorem of Milnor and Svarc then says that given a group G acting in a reasonable manner on...

open iff U ∩ X k {\displaystyle U\cap X_{k}} is open for each k-skeleton X k {\displaystyle X_{k}} . In the language of category theory, the topology on...

gauge theory and its cousins: Jacob Rasmussen's new proof of a theorem of Peter Kronheimer and Tomasz Mrowka, formerly known as the Milnor conjecture (see...