Poul Heegaard (; November 2, 1871,

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

- February 7, 1948,

Oslo Oslo ( , , or ; sma, Oslove) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population ...

) was a

Danish Danish may refer to: * Something of, from, or related to the country of Denmark People * A national or citizen of Denmark, also called a "Dane," see Demographics of Denmark * Culture of Denmark * Danish people or Danes, people with a Danish a ...

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 ...

active in the field of

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 ...

. His 1898 thesis introduced a concept now called the

Heegaard splitting In the mathematical field of geometric topology, a Heegaard splitting () is a decomposition of a compact oriented 3-manifold that results from dividing it into two handlebodies. Definitions Let ''V'' and ''W'' be handlebodies of genus ''g'', an ...

of a 3- manifold. Heegaard's ideas allowed him to make a careful critique of work of Henri Poincaré. Poincaré had overlooked the possibility of the appearance of

torsion Torsion may refer to: Science * Torsion (mechanics), the twisting of an object due to an applied torque * Torsion of spacetime, the field used in Einstein–Cartan theory and ** Alternatives to general relativity * Torsion angle, in chemistry Bi ...

in the homology groups of a space. He later co-authored, with

Max Dehn Max Wilhelm Dehn (November 13, 1878 – June 27, 1952) was a German mathematician most famous for his work in geometry, topology and geometric group theory. Born to a Jewish family in Germany, Dehn's early life and career took place in Germany. ...

, a foundational article on

combinatorial topology In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such ...

, in the form of an encyclopedia entry. Heegaard studied mathematics at the

University of Copenhagen The University of Copenhagen ( da, Københavns Universitet, KU) is a prestigious public research university in Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia after Uppsala Unive ...

, from 1889 to 1893 and following years of travelling, and teaching mathematics, he was appointed professor at University of Copenhagen in 1910. An English translation of his 1898 thesis, which laid a rigorous topological foundation for modern knot theory, may be found at https://www.maths.ed.ac.uk/~v1ranick/papers/heegaardenglish.pdf. The section on "a visually transparent representation of the complex points of an algebraic surface" is especially important. Following a dispute with the faculty over, among other things, the hiring of

Harald Bohr Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the ...

professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors ...

at the University (which Heegaard opposed);; see in particula
pp. 937–938
Heegaard accepted a professorship at

Norway Norway, officially the Kingdom of Norway, is a Nordic country in Northern Europe, the mainland territory of which comprises the western and northernmost portion of the Scandinavian Peninsula. The remote Arctic island of Jan Mayen and the ...

, where he worked till his retirement in 1941.

Notes

External links

* * *
"Heegaard home page"
1871 births 1948 deaths Danish mathematicians Topologists Presidents of the Norwegian Mathematical Society {{europe-mathematician-stub