Cracow, 2004
TROTMAN David
Professor of Mathematics
University of Provence
Marseilles, France
Telephone : 04 91 11 36 57
E-mail : trotman@cmi.univ-mrs.fr
List of publications of David TROTMAN
1. (with Christopher Zeeman), Classification of elementary catastrophes of codimension less than or equal to 5, Structural Stability, the Theory of Catastrophes, and Applications, Proceedings, Seattle 1975 (edited by P. Hilton), Lecture Notes in Math. 525, Springer, New York, 1976, 263-327.
2. A transversality property weaker than Whitney (a)-regularity, Bulletin of the London Mathematical Society 8, 1976, 225-228.
3. Geometric versions of Whitney regularity, Mathematical Proceedings of the Cambridge Philosophical Society 80, 1976, 99-101.
4. Counterexamples in stratification theory : two discordant horns, Real and Complex Singularities, Oslo 1976 (edited by P. Holm), Sijthoff & Noordhoff, Alphen aan den Rijn, 1977, 679-686.
5. Multiplicity is a C1 invariant, publication d'Orsay, 1977, 8 pages
6. Whitney stratifications : faults and detectors, Warwick thesis, 1977.
7. Interprétations topologiques des conditions de Whitney, Journées Singulières à Dijon 1978, Astérisque 59-60, 1979, 233-248.
8. Stability of transversality to a stratification implies Whitney (a)-regularity, Inventiones Math. 50, 1979, 273-277.
9. Geometric versions of Whitney regularity for smooth stratifications, Annales de l'Ecole Normale Supérieure 12, 4ème série, 1979, 453-463.
10. (with Anne Kambouchner), Whitney (a)-faults which are hard to detect, Annales de l'Ecole Normale Supérieure 12, 4ème série, 1979, 465-471.
11. (with Hans Brodersen), Whitney (b)-regularity is weaker than Kuo's ratio test for real algebraic stratifications, Mathematica Scandinavia 45, 1979, 27-34.
12. Equisingularité et conditions de Whitney, Thèse d'Etat, University of Paris-Sud, Orsay, January 1980.
13. (with Vicente Navarro Aznar), Whitney regularity and generic wings, Annales de l'Institut Fourier, Grenoble, 31, 1981, 87-111.
14. Regular stratifications and sufficiency of jets, Algebraic Geometry, La Rabida 1981 (J.-M. Aroca, R. Buchweitz, M. Giusti and M. Merle, editors), Lecture Notes in Mathematics 961, Springer, New York, 1982, 492-500.
15. Comparing regularity conditions on stratifications, Arcata 1981-Singularities, Part 2, Proceedings of Symposia in Pure Mathematics 40, American Mathematical Society, Providence, Rhode Island, 1983, 575-586.
16. (with Patrice Orro), Sur les fibres de Nash de surfaces à singularités isolées, Comptes Rendues de l'Académie des Sciences de Paris, tome 299, 1984, 397-399.
17. Transverse transversals and homeomorphic transversals, Topology 24, 1985, 25-39.
18. On the canonical Whitney stratification of real algebraic hypersurfaces, Séminaire de géométrie algébrique réelle dirigé par Jean-Jacques Risler, tome 1, Publications Mathématiques de l'Univ. Paris 7, 1986, 123-152.
19. (with Patrice Orro), On the regular stratifications and conormal structure of subanalytic sets, Bulletin of the London Mathematical Society 18, 1986, 185-191.
20. (with Karim Bekka), Propriétés métriques de familles \phi-radiales de sous-variétés différentiables, Comptes Rendues de l'Académie des Sciences de Paris, tome 305, 1987, 389-392.
21. (with Tzee-Char Kuo), On (w) and (ts)-regular stratifications, Inventiones Mathematicae 92, 1988, 633-643.
22. (with Tzee-Char Kuo and Li Pei Xin), Blowing-up and Whitney (a)-regularity, Canadian Mathematical Bulletin 32, 1989,482-485.
23. Une version microlocale de la condition (w) de Verdier, Annales de l'Institut Fourier , Grenoble, 39, 1989, 825-829.
24. On Canny's roadmap algorithm, Real Days - Symposium in honour of Aldo Andreotti (M. Galbiati, editor), University of Pisa, 1990, 115-117.
25. On Canny's roadmap algorithm : orienteering on semialgebraic sets (an application of singularity theory to theoretical robotics), Proceedings of the 1989 Warwick Singularity Theory Symposium (D. Mond and J. Montaldi, editors), Springer Lecture Notes, 1991, 320-339.
26. Blowing-up Thom-Verdier regularity, June 1991 Workshop on resolution of singularities, University of Pisa,1993, pp.117-124.
27. (with Michal Kwiecinski), Scribbling continua in Rn and constructing singularities with prescribed Nash fibre and tangent cone, Topology and its Applications, 64, 1995, 177-189.
28. La vision géométrique et son écriture, Colloque Poésie et Logique, Centre International de Poésie de Marseille, Octobre 1995.
29. (with Jean-Jacques Risler), Bilipschitz invariance of the multiplicity, Bulletin of the London Math. Soc. 29, 1997, 200-204.
30. (with Leslie Wilson, editors), Singularities of maps and differential equations, Hermann - Travaux en Cours, vol. 54, 1997, 124 pages.
31. (with Leslie Wilson, editors), Stratifications and topology of singular spaces , Hermann - Travaux en Cours, vol. 55, 1997, 107 pages.
32. Espaces stratifiés réels, Stratifications and topology of singular spaces (ed. D. Trotman et L. Wilson), Hermann - Travaux en Cours, vol. 55, 1997, 93-107.
33. Multiplicity as a C1 invariant, Real analytic and algebraic singularities, (T. Fukuda, T. Fukui, S. Izumiya, S. Koike, editors), Pitman Research Notes in Mathematics Series, vol. 381, Longman, 1998, 215-221.
34. Singularités, Dictionnaire d'Histoire et Philosophie des Sciences, edited by D. Lecourt, Presses Universitaires de France, Paris, 1999, 866-867. (pdf)
35. (with Leslie Wilson), Stratifications and finite determinacy, Proceedings of the London Math. Soc., (3) 78,1999, 334-368.
36. (with Claudio Murolo), Semi-differentiable stratified morphisms, Comptes Rendus de l'Académie des Sciences, Paris, Série I, Math. 329, 1999, no. 2, 147-152.
37. (with Laurent Noirel), Subanalytic and semialgebraic realisations of abstract stratified sets, Real Algebraic Geometry and Ordered Structures, Proceedings of the Special semester, Louisiana State University, Baton Rouge 1996 (C. Delzell, J. Madden, editors), Contemporary mathematics 253, American Mathematical Society, Providence, Rhode Island, 2000, 203-207.
38. (with Karim Bekka),Weakly Whitney stratified sets, Real and complex singularities, Sao Carlos 1998 (J.W. Bruce and F. Tari, editors), Chapman and Hall/CRC Research Notes in Mathematics 412, Boca Raton, Florida, 2000, 1-15.
39. (with Claudio Murolo), Horizontally-C1 morphisms and Thom's isotopy theorem,Comptes Rendus de l'Académie des Sciences, Paris, Série I Math. 330, 2000, no. 8, 707-712.
40. (with Patrice Orro), Cône normal à une stratification régulière, Seminari Geometria 1998-99, Università degli Studi Bologna, 12, 2000, 169-175.
41. (with Claudio Murolo), Relèvements continus contrôlés de champs de vecteurs, Bulletin des Sciences Mathématiques, 125, 2001, 253--278.(pdf)
42. (with Patrice Orro), Cône normal et régularités de Kuo-Verdier, Bulletin de la Société Mathématique de France, 130, 2002, 71-85.
43. (with Georges Comte and Pierre Milman), On Zariski's multiplicity problem, Proceedings of the Amer. Math. Soc., 130, 2002, no. 7, 2045-2048.(pdf)
44. (with Claudio Murolo and Andrew du Plessis), Stratified transversality via isotopy, 18 pages, Transactions of the Amer. Math. Soc., 355, 2003, no. 12, 4881--4900.(pdf)
45. (with Dwi Juniati and Guillaume Valette), Lipschitz stratifications and generic wings, 19 pages, Journal of the London Mathematical Society, (2) 68, 2003, 133--147.(pdf)
46. (with Karim Bekka), On metric properties of stratified sets, Manuscripta Mathematica, 111, 2003, 71-95.(pdf)
47. (with Claudio Murolo and Andrew du Plessis), Stratified transversality via time-dependent vector fields, Journal of the London Mathematical
Society, (2) 71 (2005), no. 2, 516--530.(pdf)
48. (with Dwi Juniati), Determination of Lipschitz stratifications for the surfaces ya= zbxc + xd, Singularités Franco-Japonaises, Sémin. Congr., (J.-P. Brasselet and T. Suwa, editors)10, Soc. Math. France, Paris, 2005, 127--138.(pdf)
49.
(with Leslie Wilson), (r) does not imply (n) or (npf) for definable
sets in non polynomially bounded o-minimal structures, Singularity
theory and its applications (S. Izumiya, G. Ishikawa, H. Tokunaga,
I. Shimida, T. Sano, editors), Advanced Studies in Pure Mathematics 43, Mathematical Society of Japan (2006), 463-475.(pdf)
50. (with Claudio Murolo), Semidifférentiabilité et version lisse de la conjecture de fibration de Whitney, Singularity theory and its applications (S. Izumiya, G. Ishikawa, H. Tokunaga, I. Shimida, T. Sano, editors), Advanced Studies in Pure Mathematics 43, Mathematical Society of Japan (2006), 271-309.(pdf)
51. Real stratification theory, Singularity Theory, Proceedings of the 2005 Marseille Singularity School and Conference, dedicated to Jean-Paul Brasselet on his 60th birthday (D. Chéniot, N. Dutertre, C. Murolo, A. Pichon, and D. Trotman, editors),World Scientific (2007), 139-155.(pdf)
52. (Denis Chéniot, Nicolas Dutertre, Claudio Murolo, et Anne Pichon, and David Trotman, editors), Singularity Theory, Proceedings of the 2005 Marseille Singularity School and Conference, dedicated to Jean-Paul Brasselet on his 60th birthday, World Scientific (2007), 1081 pages.
53. (with Terence Gaffney and Leslie Wilson), Equisingularity of sections, (tr) condition, and the integral closure of modules, Journal of Algebraic Geometry 18 (2009), 651-689.(pdf)
54. (with Patrice Orro), Transverse regular stratifications, Real and Complex Singularities, edited by M. Manoel, M. C. Romero Fuster and C. T. C. Wall, 10th international workshop, Sao Carlos, Brazil 2008, London Mathematical Society Lecture Note Series 380, Cambridge University Press (2010), pp. 298-304.
55. Bilipschitz equisingularity, Real and Complex Singularities, edited by M. Manoel, M. C. Romero Fuster and C. T. C. Wall, 10th international workshop, Sao Carlos, Brazil 2008, London Mathematical Society Lecture Note Series 380, Cambridge University Press (2010), pp. 338-349.
56. (with Henry King), Poincaré-Hopf theorems for singular spaces, 20 pages, submitted.(pdf)
57. (with Camille Plénat), On the multiplicities of families of complex hypersurface germs with constant Milnor number, submitted.