nLab Daniel Quillen

Daniel Quillen (1940-2011)

• Wikipedia entry

• inSpire page

• MathGenealogy page

• Eric Friedlander, Daniel Grayson (eds.): Daniel Quillen, Notices of the AMS 59 10 (2012) 1392 [pdf, full issue:pdf]

Selected writings

• Clay Mathematical Institute: Scanned images of Quillen’s research notebooks [webpage]

Introducing model category-theory for homotopy theory:

• Daniel Quillen, Homotopical algebra, Lecture Notes in Mathematics 43, Springer-Verlag 1967, iv+156 pp (doi:10.1007/BFb0097438).

On rational homotopy theory:

• Daniel Quillen: Rational homotopy theory, The Annals of Mathematics, Second Series 90 2 (1969) 205–295 [doi:10.2307/1970725, jstor:1970725, pdf]

Proof that topological realization takes Kan fibrations to Serre fibrations:

• Daniel Quillen, The geometric realization of a Kan fibration is a Serre fibration, Proc. AMS 19 (1968) 1499-1500 [doi:1968-019-06/S0002-9939-1968-0238322-1, pdf]

On the (co)homology of commutative algebras:

• D. G. Quillen, 1970, On the (co-)homology of commutative rings, in Proc. Symp. on Categorical Algebra, 65–87, American Math. Soc.

On cobordism cohomology theory:

• Daniel Quillen, Elementary Proofs of Some Results of Cobordism Theory Using Steenrod Operations, Advances in Mathematics 7 (1971), 29–56 (doi:10.1016/0001-8708(71)90041-7)

Introducing what came to be known as the Quillen metric on determinant line bundles:

• Daniel Quillen: Determinants of Cauchy-Riemann operators over a Riemann surface, Functional Analysis and its Applications 19 (1985) 31–34 [doi:10.1007/BF01086022]

On equivariant de Rham cohomology:

• Varghese Mathai, Daniel Quillen, Superconnections, Thom classes and equivariant differential forms, Topology 25, 85 (1986) (doi:10.1016/0040-9383(86)90007-8)

Also

• J. Cuntz, Daniel Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995), no. 2, 251–289, MR96c:19002, doi; Cyclic homology and nonsingularity, J. Amer. Math. Soc. 8 (1995), no. 2, 373–442, MR96e:19004, doi

On the group completion theorem:

• Daniel Quillen: On the group completion of a simplicial monoid, Appendix Q in: Eric M. Friedlander, Barry Mazur: Filtrations on the homology of algebraic varieties, Memoirs of the AMS 529 110 (1994) 89-105 [doi:10.1090/memo/0529, pdf]

Related entries

• model category, model structure on topological spaces

• Quillen's theorems

• algebraic K-theory

• quasi-free algebra

• cotangent complex

• Andre-Quillen cohomology

• Quillen-Lichtenbaum conjecture

• complex cobordism

• formal group law

• …

category: people