Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CUP PRODUCT ON RELATIVE BOUNDED COHOMOLOGY

  • HeeSook Park (Department of Mathematics Education Sunchon National University)
  • Received : 2022.07.09
  • Accepted : 2023.05.12
  • Published : 2023.07.01
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Abstract

In this paper, we define cup product on relative bounded cohomology, and study its basic properties. Then, by extending it to a more generalized formula, we prove that all cup products of bounded cohomology classes of an amalgamated free product G1 *A G2 are zero for every positive degree, assuming that free factors Gi are amenable and amalgamated subgroup A is normal in both of them. As its consequences, we show that all cup products of bounded cohomology classes of the groups ℤ * ℤ and ${\mathbb{Z}}_n\;{\ast}_{{\mathbb{Z}}_d}\;{\mathbb{Z}}_m$, where d is the greatest common divisor of n and m, are zero for every positive degree.

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References

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