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...

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

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...

(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}}...

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)...

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

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...

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

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

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

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

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

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

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

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...

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

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

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...

Weinstein (1934–2002, née Savanuck, also published as Tilla Klotz and Tilla K. Milnor) was an American mathematician known for her mentorship of younger women...

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

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

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...

William Milnor Roberts (February 12, 1810 – July 14, 1881) was an American civil engineer. Roberts was one of the most prolific and prominent civil engineers...

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...

 216–224. Gray, Abbena & Salamon 2006, p. 386. Berger 2004; Wilson 2008; Milnor 1963. Eisenhart 2004, p. 131; Berger 2004, p. 39; do Carmo 2016, p. 248;...

equivalent in the sense given above. This was originally discovered by John Milnor in the form of the exotic 7-spheres. Every one-dimensional connected smooth...

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...