nLab Isadore Singer

Isadore Manuel Singer (1924-2021)

• Wikipedia entry

• MathGenealogy page

• inSpire page

• Robert Bryant, Jeff Cheeger, Phillip Griffiths: Isadore M. Singer (1924–2021) In Memoriam Part 1: Scientific Works, Notices of the AMS (Oct 2022) [pdf]

Selected writings

Introducing the Kadison-Singer problem:

• Richard V. Kadison, Isadore Singer, Extensions of pure states, American Journal of Mathematics, 81(2):383–400, 1959 (jstor:2372748)

Generalization of the Atiyah-Jänich theorem to any degree and to KO-theory:

• Michael F. Atiyah, Isadore M. Singer, Index theory for skew-adjoint Fredholm operators, Publications Mathématiques de l’IHÉS 37 (1969) 5-26 [doi:10.1007/BF02684885, numdam:PMIHES_1969__37__5_0, pdf]

Introducing Ray-Singer analytic torsion:

• Daniel Burrill Ray, Isadore Singer: $R$-torsion and the Laplacian on Riemannian manifolds, Adv. Math. 7 2 (1971) 145-210 [doi:10.1016/0001-8708(71)90045-4]

  (for Riemannian manifolds)

• Daniel Burrill Ray, Isadore Singer: Analytic torsion for complex manifolds, Ann. Math. 98 1 (1973) 154-177 [doi:10.2307/1970909, jstor:1970909]

  (for complex manifolds)

Introducing the notion of the eta-invariant:

• Michael F. Atiyah, Vijay K. Patodi, Isadore M. Singer: Spectral asymmetry and Riemannian Geometry. I, Mathematical Proceedings of the Cambridge Philosophical Society 77 1 (1975) 43-69 [doi:10.1017/S0305004100049410, pdf]

• Michael F. Atiyah, Vijay K. Patodi, Isadore M. Singer: Spectral asymmetry and Riemannian geometry II, Mathematical Proceedings of the Cambridge Philosophical Society 78 3 (1975) 405-432 [doi:10.1017/S0305004100051872, pdf]

• Michael F. Atiyah, Vijay K. Patodi, Isadore M. Singer: Spectral asymmetry and Riemannian geometry III, Mathematical Proceedings of the Cambridge Philosophical Society 79 1 (1976) 71-99 [doi:10.1017/S0305004100052105, pdf]

On quantum anomalies via index theory:

• Michael Atiyah, Isadore Singer, Dirac operators coupled to vector potentials, Proc. Nat. Acad. Sci. USA 81, 2597-2600 (1984) (doi:10.1073/pnas.81.8.2597, jstor:23378)

On topological Yang-Mills theory:

• L. Baulieu, Isadore Singer, Topological Yang-Mills symmetry, Nuclear Physics B - Proceedings Supplements Volume 5, Issue 2, December 1988, Pages 12-19 (doi:10.1016/0920-5632(88)90366-0)

On differential cohomology with motivation from M5-branes-physics

• Michael Hopkins, Isadore Singer: Quadratic Functions in Geometry, Topology,and M-Theory, J. Differential Geom. 70 3 (2005) 329-452 [arXiv:math.AT/0211216, doi:10.4310/jdg/1143642908, euclid:1143642908]

On D=8 Yang-Mills theory:

• Laurent Baulieu, Hiroaki Kanno, Isadore Manuel Singer, Cohomological Yang-Mills Theory in Eight Dimensions (1997), Dualities in Gauge and String Theories, pp. 365-373 (1998) [arXiv:hep-th/9705127, doi:10.1142/9789814447287_0011]

category: people