Alan H. Durfee: Publications

Research Publications

  1. Foliations of odd dimensional spheres, Annals of Math. 96 (1972) 405-409
  2. (with H. B. Lawson, Jr.) Fibered knots and foliations of highly connected manifolds, Inventiones Math. 17 (1972) 203-215
  3. Fibered knots and algebraic singularities, Topology 13 (1974) 47-59
  4. The monodromy of a degenerating family of curves, Inventiones Math. 28 (1975) 231-241
  5. Knot invariants of singularities, Proc. Symp. Pure Math 29 (1975) 441-448
  6. The characteristic polynomial of the monodromy, Pacific J. Math 59 (1975) 21-26
  7. (with L. Kauffman) Periodicity of branched cyclic covers, Math. Annalen 218 (1975) 157-174
  8. Bilinear and quadratic forms on torsion modules, Advances in Math. 25 (1977) 133-164
  9. The signature of smoothings of complex surface singularities, Math. Annalen 232 (1978) 85-98
  10. Fifteen characterizations of rational double points and simple critical points, L'enseignement Math. 25 (1979) 131-163
  11. Neighborhoods of algebraic sets, Trans. Amer. Math. Soc. 276 (1983) 517-530
  12. A naive guide to mixed Hodge theory, Proc. Symp. Pure Math. 40 (1983) 313-320
  13. Low-dimensional topology of singularities, Proc. Symp. Pure Math. 40 (1983) 321-326
  14. Mixed Hodge structures on punctured neighborhoods, Duke J. Math 50 (1983) 1017-1040
  15. Four characterizations of real rational double points, L'enseignement Math. 30 (1984) 1-6. Also in Noeuds, Tresses et Singularites, Monographie 31, L'enseignement Math. (1983) 123-128.
  16. Notes on mixed Hodge theory and rational homotopy (mss. 1983)
  17. Topological restrictions on the links of isolated complex singularities, Advanced studies in Pure Math. 8 (1986). Complex analytic singularities 95- 99.
  18. Algebraic varieties which are a disjoint union of subvarieties. In: Geometry and topology: manifolds, varieties and knots, ed. Clint McCrory and Theodore Shifrin, 1987, Dekker, p. 99-102.
  19. The l-adic cohomology of links. In: Hodge theory, Proceedings Sant Cugat, Spain, 1985. Lecture notes in math. 1246, Springer (1987) 42-48.
  20. (with R. Hain) Mixed Hodge structures on the homotopy of links, Math. Ann. 280 (1988) 69-83.
  21. (with M. Saito) Mixed Hodge structures on the intersection cohomology of links, Compositio Math. 76 (1990) 49-67.
  22. The Thom-Pontrjagin invariant of a singularity, preprint 11-88 (new version in preparation).
  23. (with N. Kronenfeld, H. Munson, J. Roy and I. Westby; a paper produced at the MHC Undergraduate Summer Research Institute) Counting critical points of real polynomials in two variables, Amer. Math. Monthly 100 (1993) 255-271.
  24. Intersection homology Betti numbers, Proc. Amer. Math. Soc. 123 (1995) 989-993.
  25. The index of grad f(x,y), Topology 37 (1998) 1339-1361.
  26. Five definitions of critical point at infinity. In: Singularities, the Brieskorn Anniversary Volume, Progress in Mathematics 162 (Birkhauser 1998) 345-360.
  27. Singularities. In: History of Topology, ed. I.M. James (Elsevier 1999), 417-434.
  28. Gluing critical points (after Shustin) (preprint)
  29. (with D. O'Shea) Polynomial knots (preprint)
  30. Klein's Erlangen program (in preparation)

Educational Materials

  1. Polyhedral differential geometry (FIPSE preprint, Dec. 1993)
  2. The Alexander polynomial of a link (preprint)

Book Reviews

  1. Three-dimensional link theory and invariants of plane curve singularities by D. Eisenbud and W. Neumann, Bull. Amer. Math. Soc. 19 (1988) 481-484.
  2. The shape of space by J. Weeks, Amer. Math. Monthly 96 (1989) 660-662.

Other

  1. The summer REU project at Mount Holyoke College. In: Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs, J. Gallian, Ed., American Math. Soc. 2000, 105-115.
Last updated 1/27/08