Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE KÜNNETH ISOMORPHISM IN BOUNDED COHOMOLOGY PRESERVING THE NORMS

  • Park, HeeSook (Department of Mathematics Education Sunchon National University)
  • Received : 2019.05.31
  • Accepted : 2020.02.03
  • Published : 2020.07.31
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Abstract

In this paper, for discrete groups G and K, we show that the cohomology of the complex of projective tensor product B*(G)⨶B*(K) is isomorphic to the bounded cohomology Ĥ*(G × K) of G × K, which is the cohomology of B*(G × K) as topological vector spaces, where B*(G) is a complex of bounded cochains of G with real coefficients ℝ. In fact, we construct an isomorphism between these two cohomology groups that carries the canonical seminorm in Ĥ*(G × K) to the seminorm in the cohomology of B*(G)⨶B*(K).

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References

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