Andrew H. Wallace

Alexander Hugh Wallace (1926 – 18 January 2008) was a Scottish-American mathematician.

Biography

Wallace was born and raised in Edinburgh. He received in 1946 an MA in mathematics from Edinburgh University and in 1949 a PhD from St. Andrews University. In the 1950s he was an assistant professor of mathematics at the University of Toronto. In 1959 he became a professor at Indiana University's mathematics department, where he was also chair of the department. In 1965 he left Indiana to become a mathematics professor at the University of Pennsylvania, where he remained until his retirement as professor emeritus in 1986. For the academic year 1964–1965 and the first five months of 1968 he was a visiting scholar at the Institute for Advanced Study.

Colleagues said his mathematical work was mainly concentrated in topology where he produced fundamental results reported on principally in his series of papers entitled “Modifications and Cobounding Manifolds.” Here, he essentially settled in dimensions 5 and higher, the basic open problem regarding these geometric objects, though he did not push his results to an explicit statement of the solution. This was done by an independent method and almost simultaneously by Dr. Stephen Smale ... Dr. Wallace’s work in the topology of three dimensional spaces was groundbreaking and remains frequently cited and used to the present day.

Upon his death he was survived by his wife, three daughters and a step-daughter. His name is attached to the Lickorish-Wallace theorem.

Selected publication

Articles

• "Tangency and duality over arbitrary fields". Proceedings of the London Mathematical Society. 3 (3): 321–342. 1956.
• "On the homology theory of algebraic varieties, I". Annals of Mathematics: 248–271. 1956. JSTOR 1969608.
• "Modifications and cobounding manifolds". Can. J. Math. 12: 503–528. 1960. doi:10.4153/CJM-1960-045-7.
• "A geometric method in differential topology". Bull. Amer. Math. Soc. 68 (6): 533–542. 1962. MR 0142127.

Books

• An introduction to algebraic topology. NY: Pergamon Press. 1957.
• Homology theory on algebraic varieties. NY: Pergamon Press. 1958. reprint. Dover. 2015.
• Differential topology: first steps. NY: W. H. Benjamin. 1968. reprint. Dover. 2006.
• Algebraic topology: homology and cohomology. NY: W. H. Benjamin. 1970. reprint. Dover. 2007.

External links

• Andrew H. Wallace at the Mathematics Genealogy Project