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Proceedings of the American Mathematical Society

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The maps $ B{\rm Sp}(1)\rightarrow B{\rm Sp}(n)$

Author: Zafer Mahmud
Journal: Proc. Amer. Math. Soc. 52 (1975), 473-478
MSC: Primary 55F40
MathSciNet review: 0380794
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Abstract: Let $ Sp(n)$ be the symplectic Lie group. Then it is known that given a map $ f:BSp(1) \to BSp(1),{f^{\ast}}:{H^4}(BSp(1),{\mathbf{Z}}) \to {H^4}(BSp(1),{\mathbf{Z}})$ is zero or multiplication by the square of an odd integer. We generalise the latter part of this result using symplectic $ {K^{\ast}}$-theory.

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  • [1] J. F. Adams, Vector fields on spheres, Ann. of Math. (2) 75 (1962), 603–632. MR 0139178
  • [2] J. Frank Adams, Lectures on Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0252560
  • [3] J. F. Adams and Z. Mahmud, Classification of maps $ BG \to BG'$ (in preparation).
  • [4] M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math., Vol. III, American Mathematical Society, Providence, R.I., 1961, pp. 7–38. MR 0139181
  • [5] Armand Borel, Topics in the homology theory of fibre bundles, Lectures given at the University of Chicago, vol. 1954, Springer-Verlag, Berlin-New York, 1967. MR 0221507
  • [6] Conference on Algebraic Topology, Univ. of Illinois at Chicago Circle, Chicago, Ill., 1969. The University of Illinois at Chicago Circle, June 17-June 28, 1968. MR 0248800
  • [7] Hans Samelson, Notes on Lie algebras, Van Nostrand Reinhold Mathematical Studies, No. 23, Van Nostrand Reinhold Co., New York- London-Melbourne, 1969. MR 0254112
  • [8] N. E. Steenrod, Milgram’s classifying space of a topological group, Topology 7 (1968), 349–368. MR 0233353

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Keywords: Classifying space, Lie group, symplectic $ {K^{\ast}}$-theory, representation
Article copyright: © Copyright 1975 American Mathematical Society