André Haefliger (born 22 May 1929 in

Nyon Nyon (; outdated German: or ; outdated Italian: , ) is a municipality in Nyon District in the canton of Vaud in Switzerland. It is located some 25 kilometers north east of Geneva's city centre, and since the 1970s it has become part of the Ge ...

Switzerland ). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...

) is a

Swiss Swiss may refer to: * the adjectival form of Switzerland *Swiss people Places * Swiss, Missouri *Swiss, North Carolina * Swiss, West Virginia *Swiss, Wisconsin Other uses * Swiss-system tournament, in various games and sports * Swiss Internation ...

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 works primarily on

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 ...

Education and career

Haefliger went to school in

and then attended his final years at

Collège Calvin The Collège Calvin, formerly the Collège de Genève, is the oldest public secondary school in Geneva, Switzerland. It was founded in 1559 by John Calvin. History On February 24, 1428, the ''Conseil Général'' of Geneva decided to establish ...

Geneva Geneva ( ; french: Genève ) frp, Genèva ; german: link=no, Genf ; it, Ginevra ; rm, Genevra is the second-most populous city in Switzerland (after Zürich) and the most populous city of Romandy, the French-speaking part of Switzerland. Situa ...

. He studied mathematics at the

University of Lausanne The University of Lausanne (UNIL; french: links=no, Université de Lausanne) in Lausanne, Switzerland was founded in 1537 as a school of Protestant theology, before being made a university in 1890. The university is the second oldest in Switzer ...

from 1948 to 1952. He worked for two years as a teaching assistant at

École Polytechnique Fédérale de Lausanne École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

and then moved to

University of Strasbourg The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers. The French university traces its history to the ea ...

, where he received his Ph.D. degree in 1958. His thesis was entitled "''Structures feuilletées et cohomologie à valeurs dans un faisceau de groupoïdes''" and was written under the supervision of

Charles Ehresmann Charles Ehresmann (19 April 1905 – 22 September 1979) was a German-born French mathematician who worked in differential topology and category theory. He was an early member of the Bourbaki group, and is known for his work on the differential ...

. He got a research fellowship for one year in

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Si ...

, where he participated in the

seminar A seminar is a form of academic instruction, either at an academic institution or offered by a commercial or professional organization. It has the function of bringing together small groups for recurring meetings, focusing each time on some parti ...

Henri Cartan Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of c ...

, and then from 1959 to 1961 he worked at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of w ...

. Since 1962 he has been a full professor 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 ...

until his retirement in 1996. In 1966 Haefliger was invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rena ...

in Moscow. In 1974–75, he was president of the Swiss Mathematical Society. He obtained a Doctorate ''

honoris causa An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or ''ad hono ...

'' from the

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 ...

in 1992 and from the

University of Dijon A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...

in 1997. In 2020 Haefliger and

Martin Bridson Martin Robert Bridson is a Manx mathematician. He is the Whitehead Professor of Pure Mathematics at the University of Oxford, and President of the Clay Mathematics Institute. He was previously Head of Oxford's Mathematical Institute. He is a F ...

were awarded the American Mathematical Society's Leroy P. Steele Prize for Mathematical Exposition, for their book ''Metric Spaces of Non-Positive Curvature'' (Springer Verlag, 1999).

Research

Haefliger's main research interest are

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

and

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

. He found the topological obstruction to the existence of a

spin structure In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical ...

on an

orientable In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space i ...

Riemannian manifold In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real, smooth manifold ''M'' equipped with a positive-definite inner product ''g'p'' on the tangent space ...

. In two papers in the

Annals Annals ( la, annāles, from , "year") are a concise historical record in which events are arranged chronologically, year by year, although the term is also used loosely for any historical record. Scope The nature of the distinction between ann ...

he studied various

embedding In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X is said to be embedded in another object Y, the embedding is g ...

spheres The Synchronized Position Hold Engage and Reorient Experimental Satellite (SPHERES) are a series of miniaturized satellites developed by MIT's Space Systems Laboratory for NASA and US Military, to be used as a low-risk, extensible test bed for the ...

in relations to

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 ...

. He has also made important contributions in the theory of

foliation In mathematics (differential geometry), a foliation is an equivalence relation on an ''n''-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension ''p'', modeled on the decomposition of ...

s, introducing the notion of Haefliger structures. Eckmann Hilton Serre Haefliger

He wrote more than 80 papers in peer review journals and had 20 Ph.D. students, including Augustin Banyaga and the future Field Medalist

Vaughan Jones Sir Vaughan Frederick Randal Jones (31 December 19526 September 2020) was a New Zealand mathematician known for his work on von Neumann algebras and knot polynomials. He was awarded a Fields Medal in 1990. Early life Jones was born in Gis ...

Selected works

*
"Travaux de Novikov sur les feuilletages." Séminaire Bourbaki 10 (1966-1968): 433-444."Sur les classes caractéristiques des feuilletages." Séminaire Bourbaki 14 (1971-1972): 239-260."Sphères d'homotopie nouées." Séminaire Bourbaki 9 (1964-1966): 57-68. "Feuilletages riemanniens." Séminaire Bourbaki 31 (1988-1989): 183-197."Plongements de variétés dans le domaine stable." Séminaire Bourbaki 8 (1962-1964): 63-77.
* * * * * * * (Ph.D. Thesis) * * * * *

References

External links

* * * {{DEFAULTSORT:Haefliger, Andre Swiss mathematicians 1929 births Living people University of Strasbourg alumni University of Geneva faculty Topologists Institute for Advanced Study people People from Nyon University of Lausanne alumni