Michel Kervaire
Encyclopedia
Michel André Kervaire was a French
mathematician
who made significant contributions to topology
and algebra
. He was the first to show the existence of topological n-manifolds with no differentiable structure (using the Kervaire invariant), and (with John Milnor
) computed the number of exotic sphere
s in dimensions greater than four. He is also well known for fundamental contributions to high-dimensional knot theory
. The solution of the Kervaire invariant problem was announced by Hopkins
in Edinburgh on 21 April 2009.
He was the son of André Kervaire (a French industrialist) and Nelly Derancourt. After completing high school in France
, Kervaire pursued his studies at ETH Zurich
(1947–1952), receiving a Ph.D.
in 1955. His thesis, entitled Courbure intégrale généralisée et homotopie, was written under the direction of Heinz Hopf
.
He was a professor at New York University
's Courant Institute
from 1959 to 1971, and then at the University of Geneva
from 1971 to 1997, when he retired. He was an honorary member of the Swiss Mathematical Society
.
s on an n-sphere for n > 4.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who made significant contributions to topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
and algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
. He was the first to show the existence of topological n-manifolds with no differentiable structure (using the Kervaire invariant), and (with John Milnor
John Milnor
John Willard Milnor is an American mathematician known for his work in differential topology, K-theory and dynamical systems. He won the Fields Medal in 1962, the Wolf Prize in 1989, and the Abel Prize in 2011. Milnor is a distinguished professor at Stony Brook University...
) computed the number of exotic sphere
Exotic sphere
In differential topology, a mathematical discipline, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere...
s in dimensions greater than four. He is also well known for fundamental contributions to high-dimensional knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
. The solution of the Kervaire invariant problem was announced by Hopkins
Michael J. Hopkins
Michael Jerome Hopkins is an American mathematician known for work in algebraic topology.-Life:He received his Ph.D. from Northwestern University in 1984 under the direction of Mark Mahowald. In 1984 he also received his D.Phil...
in Edinburgh on 21 April 2009.
He was the son of André Kervaire (a French industrialist) and Nelly Derancourt. After completing high school in France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
, Kervaire pursued his studies at ETH Zurich
ETH Zurich
The Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
(1947–1952), receiving a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1955. His thesis, entitled Courbure intégrale généralisée et homotopie, was written under the direction of Heinz Hopf
Heinz Hopf
Heinz Hopf was a German mathematician born in Gräbschen, Germany . He attended Dr. Karl Mittelhaus' higher boys' school from 1901 to 1904, and then entered the König-Wilhelm- Gymnasium in Breslau. He showed mathematical talent from an early age...
.
He was a professor at New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
's Courant Institute
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences is an independent division of New York University under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics...
from 1959 to 1971, and then at the University of Geneva
University of Geneva
The University of Geneva is a public research university located in Geneva, Switzerland.It was founded in 1559 by John Calvin, as a theological seminary and law school. It remained focused on theology until the 17th century, when it became a center for Enlightenment scholarship. In 1873, it...
from 1971 to 1997, when he retired. He was an honorary member of the Swiss Mathematical Society
Swiss Mathematical Society
The Swiss Mathematical Society , founded in Basel on September 4, 1910, is the national mathematical society of Switzerland and a member society of the European Mathematical Society. Although now published by the European Mathematical Society, Commentarii Mathematici Helvetici began in 1929 with...
.
Selected publications
This paper describes the structure of the group of smooth structureSmooth structure
In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows one to perform mathematical analysis on the manifold....
s on an n-sphere for n > 4.
External links
- Michel Kervaire's work in surgery and knot theory (Slides of lectures given by Andrew Ranicki at the Kervaire Memorial Symposium, Geneva, February 2009).