André Haefliger (; 22 May 19297 March 2023) was a Swiss mathematician who worked primarily on

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

Education and career

Haefliger went to school in

Nyon Nyon (; historically German language, German: or and Italian language, Italian: , ) is a Municipalities of Switzerland, municipality in Nyon District in the Cantons of Switzerland, canton of Vaud in Switzerland. It is located some 25 kilometer ...

and then attended his final years at

Collège de Genève In France, secondary education is in two stages: * ''Collèges'' () cater for the first four years of secondary education from the ages of 11 to 14. * ''Lycées'' () provide a three-year course of further secondary education for students between ...

Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...

. He studied mathematics at the

University of Lausanne The University of Lausanne (UNIL; ) 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 Switzerland, and one of the oldest universities ...

from 1948 to 1952. He worked for two years as a teaching assistant at École Polytechnique de l'Université de Lausanne. He then moved to

University of Strasbourg The University of Strasbourg (, Unistra) is a public research university located in Strasbourg, France, with over 52,000 students and 3,300 researchers. Founded in the 16th century by Johannes Sturm, it was a center of intellectual life during ...

, then he followed

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 differentia ...

in Paris, 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

. Haefliger got a

research fellowship A research fellow is an academic research position at a university or a similar research institution, usually for list of academic ranks, academic staff or faculty members. A research fellow may act either as an independent investigator or under ...

for one year at the

University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...

, 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 part ...

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) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...

. Since 1962 he has been a full professor at the

University of Geneva The University of Geneva (French: ''Université de Genève'') is a public university, public research university located in Geneva, Switzerland. It was founded in 1559 by French theologian John Calvin as a Theology, theological seminary. It rema ...

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 IMU Abacus Medal (known before ...

in Moscow. In 1974–75, he was president of the

Swiss Mathematical Society The Swiss Mathematical Society, SMS (, SMG; ), founded in Basel on 4 September 1910, is the national mathematical society of Switzerland. It is a member of the European Mathematical Society. History The SMS was established on 4 September 1910 ...

. Haefliger 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 ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran ...

in 1992 and from the

University of Dijon A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...

in 1997. In 2020 Haefliger and Martin Bridson 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). Haefliger died on 7 March 2023, at the age of 93.

Research

Haefliger's main research interests were

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 a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

. Haefliger 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 mathemati ...

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 "anticlockwise". A space is o ...

Riemannian manifold In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. Euclidean space, the N-sphere, n-sphere, hyperbolic space, and smooth surf ...

. In two papers in the

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

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 (mathematics), group that is a subgroup. When some object X is said to be embedded in another object Y ...

sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

s in relations to

knot theory In topology, knot theory is the study of knot (mathematics), 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 be und ...

. He has also made important contributions in the theory of

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

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 Augustin Banyaga (born March 31, 1947) is a Rwandan-born American mathematician whose research fields include symplectic topology and contact geometry. He is currently a Professor of Mathematics at Pennsylvania State University. Biography While ...

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 Gisbo ...

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 1929 births 2023 deaths Swiss mathematicians University of Strasbourg alumni University of Lausanne alumni Academic staff of the University of Geneva Topologists Institute for Advanced Study people People from Nyon University of Paris alumni