On the Contribution of Wu Wen-Tsün to Algebraic Topology View Full Text


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Article Info

DATE

2019-02

AUTHORS

Jean-Paul Brasselet

ABSTRACT

The aim of this article is to present the contribution of Wu Wen-Tsün to Algebraic Topology and more precisely to the theory of characteristic classes. Several papers provide complete and welldocumented biography and academic career of Wu Wen-Tsün, in particular, Hudecek, 2014; O’Connor and Robertson, 2006; Wen-Tsün Wu’s Academic Career, 2006; Selected works of Wen-Tsun Wu, 2008. The author does not repeat the details provided in these papers concerning the Wu Wen-Tsün’s bibliography, we will just mention people involved in the Wu Wen-Tsün’s period in France. In addition to Wu Wen-Tsün’s papers, the Dieudonné’s book (Dieudonné, 1960) provides an excellent presentation of main results of Wu Wen-Tsün in Algebraic and Differential Topology. The author will use and abuse of this book (and refer to) when suitable. In the introduction, the author recalls mainly historical facts concerning the contribution of Wu Wen-Tsün to Algebraic Topology. The second section shows specifically the contribution of Wu Wen-Tsün to the Stiefel-Whitney classes and introduces the third section, dealing with the (real) Wu classes. The author provides definition, properties as well as further developments and generalizations of the Wu classes. The fourth and fifth sections are devoted to recent applications: In Cobordism theory and in Mathematical Physics. The author notices that Wu classes have been used as well in other domains, in particular surgery theory (Madsen and Milgram, 1979). The last section concerns the complex Wu classes and shows that the more recent Mather classes coincide with the previously defined complex Wu classes, that is a result from Zhou (1994) (see also Liu, 1996). This article is devoted to the contribution of Wu Wen-Tsün to the theory of Characteristic Classes, which coincides with his “French period” (1947–1951). However, speaking of Algebraic Topology, it is worthwhile to mention the important contribution of Wu Wen-Tsün to the Theory of realization of complexes or manifolds in Euclidean spaces and of embedding classes. That coincides with his return to China (1956–1965). More... »

PAGES

3-36

References to SciGraph publications

  • 1961-12. Cohomologie-Operationen und charakteristische Klassen in MATHEMATISCHE ZEITSCHRIFT
  • 1983-02. Intersection homology II in INVENTIONES MATHEMATICAE
  • 1935-12. Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten in COMMENTARII MATHEMATICI HELVETICI
  • 1984-12. Intersection homology operations in COMMENTARII MATHEMATICI HELVETICI
  • 1992. Manifolds and Modular Forms in NONE
  • 1971. Combinatorial invariants of analytic spaces in PROCEEDINGS OF LIVERPOOL SINGULARITIES — SYMPOSIUM I
  • 1987-09. On Chern numbers of algebraic varieties with arbitrary singularities in ACTA MATHEMATICA SINICA, ENGLISH SERIES
  • 1954-12. Quelques propriétés globales des variétés différentiables in COMMENTARII MATHEMATICI HELVETICI
  • 1966. Topological Methods in Algebraic Geometry in NONE
  • 1956-12. Vollständigkeit der Wuschen Relationen zwischen den Stiefel-Whitneyschen Zahlen differenzierbarer Mannigfaltigkeiten in MATHEMATISCHE ZEITSCHRIFT
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    http://scigraph.springernature.com/pub.10.1007/s11424-019-8342-6

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    http://dx.doi.org/10.1007/s11424-019-8342-6

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    45 schema:description The aim of this article is to present the contribution of Wu Wen-Tsün to Algebraic Topology and more precisely to the theory of characteristic classes. Several papers provide complete and welldocumented biography and academic career of Wu Wen-Tsün, in particular, Hudecek, 2014; O’Connor and Robertson, 2006; Wen-Tsün Wu’s Academic Career, 2006; Selected works of Wen-Tsun Wu, 2008. The author does not repeat the details provided in these papers concerning the Wu Wen-Tsün’s bibliography, we will just mention people involved in the Wu Wen-Tsün’s period in France. In addition to Wu Wen-Tsün’s papers, the Dieudonné’s book (Dieudonné, 1960) provides an excellent presentation of main results of Wu Wen-Tsün in Algebraic and Differential Topology. The author will use and abuse of this book (and refer to) when suitable. In the introduction, the author recalls mainly historical facts concerning the contribution of Wu Wen-Tsün to Algebraic Topology. The second section shows specifically the contribution of Wu Wen-Tsün to the Stiefel-Whitney classes and introduces the third section, dealing with the (real) Wu classes. The author provides definition, properties as well as further developments and generalizations of the Wu classes. The fourth and fifth sections are devoted to recent applications: In Cobordism theory and in Mathematical Physics. The author notices that Wu classes have been used as well in other domains, in particular surgery theory (Madsen and Milgram, 1979). The last section concerns the complex Wu classes and shows that the more recent Mather classes coincide with the previously defined complex Wu classes, that is a result from Zhou (1994) (see also Liu, 1996). This article is devoted to the contribution of Wu Wen-Tsün to the theory of Characteristic Classes, which coincides with his “French period” (1947–1951). However, speaking of Algebraic Topology, it is worthwhile to mention the important contribution of Wu Wen-Tsün to the Theory of realization of complexes or manifolds in Euclidean spaces and of embedding classes. That coincides with his return to China (1956–1965).
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