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Italo Jose Dejter (Bahia Blanca, 1939) is an Argentine-born American mathematician of Bessarabian Jewish descent. He is a professor at the University of Puerto Rico (UPRRP)〔 since 1984, having conducted research in mathematics, particularly in areas that include algebraic topology, differential topology, graph theory, coding theory and design theory. He has an Erdos number of 2〔 since 1993.〔Brouwer A. E.; Dejter I. J.; Thomassen C. "Highly symmetric subgraphs of hypercubes", J. Algebraic Combinat. 2, 22-25, 1993〕 Dejter completed the Licentiate degree in Mathematics from University of Buenos Aires in 1967, and the Ph.D. degree in Mathematics from Rutgers University in 1975 under the supervision of Ted Petrie.〔 He was a professor at Federal University of Santa Catarina, Brazil, from 1977 to 1984. Dejter has been a visiting scholar at a number of research institutions, including University of São Paulo, Instituto Nacional de Matemática Pura e Aplicada, Federal University of Rio Grande do Sul, University of Cambridge, National Autonomous University of Mexico, Simon Fraser University, University of Victoria, New York University, University of Illinois at Urbana–Champaign, McMaster University, DIMACS, Autonomous University of Barcelona, Technical University of Denmark, Auburn University, Polytechnic University of Catalonia, Technical University of Madrid, Charles University, Ottawa University, Simón Bolívar University, etc. The sections below describe the relevance of Dejter's work in the research areas mentioned in the first paragraph above, or in the box to the right. ==Algebraic and differential topology== In 1971, Ted Petrie〔Petrie T. "Smooth S1-actions on homotopy complex projective spaces and related topics", Bull. Amer. Math. Soc. 78 (1972) 105–153〕 conjectured that if X is a closed, smooth 2''n''-dimensional homotopy complex projective space that admits a nontrivial smooth action of the circle, and if a function h, mapping X onto the 2''n''-dimensional complex projective space, is a homotopy equivalence, then h preserves the Pontrjagin classes. In 1975, Dejter〔Dejter I. J. "Smooth S1-manifolds in the homotopy type of CP3 ", Mich. Math. Jour. 23 (1976), 83–95〕 proved Petrie's Conjecture for n=3, establishing this way that every closed, smooth, 6-dimensional homotopy complex projective space must be the complex 3-dimensional projective space CP3. Dejter's result is most relevant in view of Petrie's exotic S1-actions on CP3,〔Petrie T. "Exotic S1-actions on CP3 and related topics", Invent. Math. 17 (1972), 317–327.〕 (apart from the trivial S1-actions on CP3). Let G be a compact Lie group, let Y be a smooth G-manifold and let F a G-fibre map between G-vector bundles of the same dimension over Y which on each G-fibre is proper and has degree one. Petrie〔 also asked: What are necessary and sufficient conditions for the existence of a smooth G-map properly G-homotopic to F and transverse to the zero-section? Dejter〔Dejter I. J. "G-Transversality to CP^n", Springer-Verlag Lecture Notes in Mathematics, 652 (1976), 222–239〕 provided both types of conditions, which do not close to a necessary and sufficient condition due to a counterexample.〔 The main tool involved in establishing the results above by reducing differential-topology problems into algebraic-topology solutions is equivariant algebraic K-theory, where equivariance is understood with respect to the group given by the circle, i.e. the unit circle of the complex plane. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Italo Jose Dejter」の詳細全文を読む スポンサード リンク
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