nLab Graeme Segal

Selected writings

Wikimedia Commons image, taken by

George Bergman

in 1982

Selected writings

On classifying spaces and spectral sequences (and introducing, following Grothendicek 61, the “Segal conditions”, see also at complete Segal space):

• Graeme Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math., vol. 34, pp. 105–112 (1968)
• Graeme Segal, The representation ring of a compact Lie group, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, January 1968, Volume 34, Issue 1, pp 113-128 (numdam:PMIHES_1968__34__113_0)

On the group completion theorem:

• Graeme Segal, Equivariant K-theory, Inst. Hautes Etudes Sci. Publ. Math. No. 34 (1968) p. 129-151
• Michael Atiyah, Graeme Segal, Equivariant $K$-theory and completion, J. Differential Geom. Volume 3, Number 1-2 (1969), 1-18. (Euclid)

On equivariant stable homotopy theory and the isomorphism between the Burnside ring and the equivariant stable Cohomotopy of the point:

• Graeme Segal, Equivariant stable homotopy theory, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, pp. 59–63. Gauthier-Villars, Paris, 1971 (pdf)
• Graeme Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973), 213–221. MR 0331377 (pdf)

On the Kahn-Priddy theorem (and a pre-cursor of Snaith's theorem):

On K-theory of permutative categories, Gamma spaces as models for connective spectra, and the identification of stable Cohomotopy with the K-theory of finite sets:

On the homotopy type of spaces of rational functions from the Riemann sphere to itself (related to the moduli space of monopoles in $\mathbb{R}^3$ and to the configuration space of points in $\mathbb{R}^2$):

• Graeme Segal, Two-dimensional conformal field theories and modular functors, in: IXth International Congress on Mathematical Physics (Swansee 1988), Hilger, Bristol 1989, pp. 22-37

On the functorial-definition of 2d conformal field theory:

• Graeme Segal, The definition of conformal field theory, Topology, geometry and quantum field theory London Math. Soc. Lecture Note Ser., 308, Cambridge Univ. Press, Cambridge, (2004), 421-577 (pdf)

On quantization of the electromagnetic field in view of Dirac charge quantization and higher U(1)-gauge theory:

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