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Grafting Boardman’s cherry trees to quantum field theory. (English) Zbl 0938.55023

Meyer, Jean-Pierre (ed.) et al., Homotopy invariant algebraic structures. A conference in honor of J. Michael Boardman. AMS special session on homotopy theory, Baltimore, MD, USA, January 7-10, 1998. Providence, RI: American Mathematical Society. Contemp. Math. 239, 19-27 (1999).
Summary: Michael Boardman has been a major contributor to the theory of infinite loop spaces and higher homotopy algebra. Indeed Boardman was the first to refer to ‘homotopy everything’. One particular contribution which has had major progeny is his use of ‘geometric’ trees, combinatorial trees with lengths attached to edges. Here is a modified version of the talk given to honor Mike on the occasion of his 60th birthday. It is an idiosyncratic survey of parts of homotopy algebra from PoincarĂ© to the present day, with emphasis on Boardman’s original ideas, starting with his cubical subdivision of the associahedra through recent applications in mathematical physics via compactifications of moduli spaces.
For the entire collection see [Zbl 0924.00035].

MSC:

55P99 Homotopy theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
14H15 Families, moduli of curves (analytic)
55P35 Loop spaces
18A10 Graphs, diagram schemes, precategories
18C99 Categories and theories
57R56 Topological quantum field theories (aspects of differential topology)
55-03 History of algebraic topology
01A60 History of mathematics in the 20th century

Biographic References:

Boardman, J. M.
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