The Lickorish-Wallace theorem establishes that every closed orientable 3-manifold is attainable through Dehn surgery on a link, a fundamental result in geometric topology. William Bernard Raymond Lickorish, a British mathematician, spent his career analyzing the complexities of knots and links, shaping the modern understanding of low-dimensional topology through his rigorous research and academic contributions.
Academic Foundation and Research
Born on 19 February 1938, W. B. R. Lickorish pursued his higher education at the University of Cambridge. In 1964, he completed his doctoral thesis under the supervision of Christopher Zeeman. His early academic work, such as his 1962 paper titled A Representation of Orientable Combinatorial 3-Manifolds, laid the groundwork for his later proofs. He eventually served as an emeritus professor of geometric topology within the Department of Pure Mathematics and Mathematical Statistics at Cambridge and held an emeritus fellowship at Pembroke College.
Twenty questions, eight minutes on the clock, and a percentile measured against everyone who has taken it. No sign-up.
Take the IQ test →Advances in Knot Theory
Lickorish became recognized for his contributions to knot theory, specifically as a co-discoverer of the HOMFLY polynomial, a significant invariant for links. His collaborative research, notably the 1985 paper A New Polynomial Invariant of Knots and Links published in the Bulletin of the American Mathematical Society, advanced the field's mathematical machinery. In 1997, he authored the textbook An Introduction to Knot Theory, published by Springer as part of the Graduate Texts in Mathematics series.
Professional Recognition
The mathematical community acknowledged his achievements with several distinctions. In 1991, he was awarded the Senior Whitehead Prize by the London Mathematical Society. During that same year, he and Kenneth Millett received the Chauvenet Prize for their collaborative work on polynomial invariants. More recently, the American Mathematical Society selected Lickorish for the 2019 class of fellows, citing his impact on knot theory and low-dimensional topology.
Fast facts
- Full name: William Bernard Raymond Lickorish
- Born: 19 February 1938
- Citizenship: United Kingdom
- Doctoral supervisor: Christopher Zeeman
- Academic home: University of Cambridge
- Key theorem: Lickorish-Wallace theorem
- 1991 Award: Senior Whitehead Prize
- 2019 Membership: Fellow of the American Mathematical Society
Questions readers ask
What is the primary focus of Lickorish's mathematical research?
His work centers on topology, specifically geometric topology and knot theory.
Which major awards has he received?
He is the recipient of the 1991 Senior Whitehead Prize, the 1991 Chauvenet Prize, and was named a fellow of the American Mathematical Society in 2019.
Achievements
- Senior Whitehead Prize — 1991
- Fields: topology
