Michel André Kervaire (26 April 1927 – 19 November 2007) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who made significant contributions to

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

and

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

. He introduced the Kervaire semi-characteristic. He was the first to show the existence of topological ''n''-

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...

s with no

differentiable structure In mathematics, an ''n''-dimensional differential structure (or differentiable structure) on a set ''M'' makes ''M'' into an ''n''-dimensional differential manifold, which is a topological manifold with some additional structure that allows for dif ...

(using the Kervaire invariant), and (with

John Milnor John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Univ ...

) computed the number of

exotic sphere In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold ''M'' that is homeomorphic but not diffeomorphic to the standard Euclidean ''n''-sphere. That is, ''M'' is a sphere from the point of view of a ...

s in dimensions greater than four. He is also well known for fundamental contributions to high-dimensional

knot theory In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...

. The solution of the Kervaire invariant problem was announced by Michael Hopkins in

Edinburgh Edinburgh ( ; gd, Dùn Èideann ) is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. Historically part of the county of Midlothian (interchangeably Edinburghshire before 1921), it is located in Lothian ...

on 21 April 2009.

Education

He was the son of André Kervaire (a French industrialist) and Nelly Derancourt. After completing high school in

France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...

, Kervaire pursued his studies at

ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , a ...

(1947–1952), receiving a Ph.D. in 1955. His thesis, entitled ''Courbure intégrale généralisée et homotopie'', was written under the direction of

Heinz Hopf Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of topology and geometry. Early life and education Hopf was born in Gräbschen, Germany (now , part of Wrocław, Poland), the son of Eliza ...

and

Beno Eckmann Beno Eckmann (31 March 1917 – 25 November 2008) was a Swiss mathematician who made contributions to algebraic topology, homological algebra, group theory, and differential geometry. Life Born in Bern, Eckmann received his master's degree from ...

Career

Kervaire was a professor at

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then- Secretary of the Treasury Albert Gallatin. In 1832, th ...

Courant Institute The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

from 1959 to 1971, and then at the

University of Geneva The University of Geneva (French: ''Université de Genève'') is a public research university located in Geneva, Switzerland. It was founded in 1559 by John Calvin as a theological seminary. It remained focused on theology until the 17th centur ...

from 1971 to 1997, when he retired. He received an honorary doctorate from the

University of Neuchâtel The University of Neuchâtel (UniNE) is a French-speaking university based in Neuchâtel, Switzerland. The university has four faculties (schools) and more than a dozen institutes, including arts and human sciences, natural sciences, law and eco ...

in 1986; he was also an honorary member of the Swiss Mathematical Society.

Selected publications

* * This paper describes the structure of the group of

smooth 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. Definition A smooth structure on a manifold M is ...

s on an ''n''-sphere for ''n'' > 4. * * *

Notes

References

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) {{DEFAULTSORT:Kervaire, Michel 20th-century French mathematicians 20th-century Swiss mathematicians Topologists Algebraists Courant Institute of Mathematical Sciences faculty ETH Zurich alumni People from Częstochowa 1927 births 2007 deaths University of Geneva faculty Swiss expatriates in the United States