In mathematics, Milnor maps are named in honor of John Milnor, who introduced them to topology and algebraic geometry in his book Singular Points of Complex...

John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional...

3 = 0 {\displaystyle z^{2}+w^{3}=0} . Then this fiber bundle has the Milnor map ϕ ( z , w ) = ( z 2 + w 3 ) / | z 2 + w 3 | {\displaystyle \phi (z...

curvature Milnor construction Milnor K-theory Milnor fibration Milnor invariants Milnor manifold Milnor map Milnor–Moore theorem Milnor number Milnor ring...

isolated critical point of a real-polynomial map F: R4→R2, so (according to a theorem of John Milnor) the Milnor map of F is actually a fibration. Bernard Perron...

(hence the name "exotic"). The first exotic spheres were constructed by John Milnor (1956) in dimension n = 7 {\displaystyle n=7} as S 3 {\displaystyle S^{3}}...

its investigations. His work in complex singularity theory generalized Milnor maps into an algebraic setting and extended the Picard-Lefschetz formula beyond...

multiplicity two and the tangent cone is not singular outside its vertex. Milnor map Resolution of singularities Singular point of a curve Singularity theory...

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)...

manifold, but vanishes on all smooth manifolds of dimension 10. Kervaire & Milnor (1963) computes the group of exotic spheres (in dimension greater than 4)...

mathematics, especially differential topology and cobordism theory, a Kervaire–Milnor group is an abelian group defined as the h-cobordism classes of homotopy...

mathematical subject of geometric group theory, the Švarc–Milnor lemma (sometimes also called Milnor–Švarc lemma, with both variants also sometimes spelling...

was first described by John Milnor and subsequently used extensively in surgery theory to produce manifolds and normal maps with given surgery obstructions...

called the Galois symbol map. The relation between étale (or Galois) cohomology of the field and Milnor K-theory modulo 2 is the Milnor conjecture, proven by...

the Milnor number, named after John Milnor, is an invariant of a function germ. If f is a complex-valued holomorphic function germ then the Milnor number...

The Milnor–Thurston kneading theory is a mathematical theory which analyzes the iterates of piecewise monotone mappings of an interval into itself. The...

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

similar properties, but different from the Hopf fibrations, were used by John Milnor to construct exotic spheres. The Hopf fibration has many implications, some...

embedding Link concordance Link group Link (knot theory) Milnor conjecture (topology) Milnor map Möbius energy Mutation (knot theory) Physical knot theory...

Comptes rendus de l'Académie des sciences, 166: 26–28 Milnor, John Willard (2006), "On Lattès maps", Dynamics on the Riemann sphere, Eur. Math. Soc., pp...

dimensions. Such a generalization was used by Michael Barratt and John Milnor to provide examples of compact, finite-dimensional spaces with nontrivial...

M. (1976). Differential topology. Springer-Verlag. ISBN 0-387-90148-5. Milnor, J.W. (1997). Topology from the Differentiable Viewpoint. Princeton University...

topology, the Milnor–Wood inequality is an obstruction to endow circle bundles over surfaces with a flat structure. It is named after John Milnor and John...

group laws Crossed module Milnor's theorem on Kan complexes Fibration of simplicial sets May, Ch. 8. § 3. May, Ch 4. § 5. Milnor 1959, Corollary 1. NB: "second...

analogues of the Poincaré conjecture, had been done earlier by René Thom, John Milnor, Stephen Smale and Sergei Novikov. A very pervasive and flexible technique...

example was constructed by John Milnor in dimension 7. He constructed a smooth 7-dimensional manifold (called now Milnor's sphere) that is homeomorphic to...

manifold from another in a 'controlled' way, introduced by John Milnor (1961). Milnor called this technique surgery, while Andrew Wallace called it spherical...

complex quadratic mappings Mandelbrot set Julia set Milnor–Thurston kneading theory Tent map Logistic map Poirier, Alfredo (1993). "On postcritically finite...

then Hom(X,Y) is homotopy equivalent to a CW complex by a theorem of John Milnor (1959). Note that X and Y are compactly generated Hausdorff spaces, so Hom(X...

K_{j}^{M}(k)\cong H^{j}(k,\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...