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SOME REMARKS ON BOUNDED COHOMOLOGY GROUP OF PRODUCT OF GROUPS

  • Park, HeeSook (Department of Mathematics Education, SunChon National University)
  • Received : 2019.02.25
  • Accepted : 2019.04.19
  • Published : 2019.09.25

Abstract

In this paper, for discrete groups G and K, we show that the bounded cohomology group of $G{\times}K$ is isomorphic to the cohomology group of the complex of the projective tensor product $B^*(G){\hat{\otimes}}B^*(K)$, where $B^*(G)$ and $B^*(G)$ are the complexes of bounded cochains with real coefficients ${\mathbb{R}}$ of G and K, respectively.

Keywords

bounded cohomology;tensor product;relatively injective

References

  1. J. Cigler, V. Losert, P. Michor, Banach modules and functors on categories of Banach spaces, Marcel Dekker, Inc., 1979.
  2. N. Ivanov, Foundation of theory of bounded cohomology, Journal of Soviet Math., 37, 1987, 1090-1114. https://doi.org/10.1007/BF01086634
  3. S. Mac Lane, Homology, 4th Printing, Springer, 1994.
  4. H. Park, The Kunneth Spectral sequence for complexes of Banach spaces, J. Korean Math. Soc. 55, No 4, 2018, 809-832 https://doi.org/10.4134/JKMS.J170464
  5. J. Rotman, Introduction to Homological Algebra, Academic Press Inc., 1979.
  6. R. A. Ryan, Introduction to Tensor Products of Banach Spaces, Springer, 2002.