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The extension problem and the mod 2 cohomology of the space of loops on Spin (N)

Published online by Cambridge University Press:  14 November 2011

Katsuhiko Kuribayashi
Katsuhiko Kuribayashi
Affiliation:
Department of Mathematics, Gunma College of Technology, 580 Toribamachi, Maebashi, Gunma 371, Japan
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Synopsis

Let {Er, dr} be a spectral sequence converging to a Hopf algebra H*. We give a method of reconstructing H* from E∞**. By using our method, we determine the mod 2 cohomology of the space of loops on a simply-connected space whose mod 2 cohomology is isomorphic to that of Spin(N) as an algebra over the Steenrod algebra.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 121 , Issue 1-2 , 1992 , pp. 91 - 99
Copyright
Copyright © Royal Society of Edinburgh 1992

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References

1Bott, R.. The space of loops on a Lie group. Michigan Math. J. 5 (1958), 36–61.CrossRefGoogle Scholar
2Eilenberg, S. and Moore, J. C.. Homology and fibration I, Coalgebras, cotensor product and its derived functors. Comment Math. Helv. 40 (1966), 199–236.CrossRefGoogle Scholar
3Ishitoya, K., Kono, A. and Toda, H.. Hopf algebra structure of mod 2 cohomology of simple Lie groups. Publ. Res. Inst. Math. Sci. 12 (1976), 141–167.CrossRefGoogle Scholar
4Kane, R. M.. On loop spaces without p torsion. Pacific J. Math. 60 (1975), 189–201.CrossRefGoogle Scholar
5May, J. P. and Zabrodsky, A.. H *(Spin (n)) as a Hopf algebra. J. Pure Appl. Algebra 10 (1977), 193–200.CrossRefGoogle Scholar
6McCleary, J. and Ziller, W.. On the free loop space of homogeneous spaces. Amer. J. of Math. 109 (1987), 765–782.CrossRefGoogle Scholar
7Milnor, J. W. and Moore, J. C.. On the structure of Hopf algebras. Ann. of Math. 81 (1965), 211–236.CrossRefGoogle Scholar
8Rector, D. L.. Steenrod operations in the Eilenberg-Moore spectral sequence. Comment Math. Helv. 45 (1970), 540–552.CrossRefGoogle Scholar
9Smith, L.. Homological algebra and Eilenberg-Moore spectral sequence. Trans. Amer. Math. Soc. 129 (1967), 58–93.CrossRefGoogle Scholar
10Smith, L.. Lectures on the Eilenberg–Moore spectral sequence, Lecture Notes in Mathematics 134 (Berlin: Springer, 1969).Google Scholar
11Smith, L.. On the Künneth theorem I. Math. Z. 166 (1970), 94–140.CrossRefGoogle Scholar