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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.
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참고문헌 (6)
참고문헌 신청
J. Cigler / 1979 / Banach modules and functors on categories of Banach spaces / Marcel Dekker, Inc
N. Ivanov / 1987 / Foundation of theory of bounded cohomology / Journal of Soviet Math 37:1090~1114
S. Mac Lane / 1994 / Homology / Springer
박희숙 / 2018 / The K\"{u}nneth spectral sequence for complexes of Banach spaces / 대한수학회지 55(4):809~832
J. Rotman / 1979 / Introduction to Homological Algebra / Academic Press Inc.
N. Ivanov / 1987 / Foundation of theory of bounded cohomology / Journal of Soviet Math 37:1090~1114
S. Mac Lane / 1994 / Homology / Springer
박희숙 / 2018 / The K\"{u}nneth spectral sequence for complexes of Banach spaces / 대한수학회지 55(4):809~832
J. Rotman / 1979 / Introduction to Homological Algebra / Academic Press Inc.
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