SOME REMARKS FOR KÜNNETH FORMULA ON BOUNDED COHOMOLOGY

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 1,  2015, pp.7-27
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.1.7
Title & Authors
SOME REMARKS FOR KÜNNETH FORMULA ON BOUNDED COHOMOLOGY
Park, HeeSook;

Abstract
Kuneth formula is to compute (co)-homology of $\small{A{\otimes}B}$ for known (co)-homology of the complexes A and B. In the ordinary case, this is done by using elementary homological methods in an abelian category. However, when we consider the bounded cochain complex with values in $\small{\mathbb{R}}$ and its structure as a real Banach space, the techniques of homological algebra for constructing K$\small{\ddot{u}}$nneth type formulas on it are not effective. The most notable facts are the image of a morphism of Banach spaces is not necessarily closed, and also the closed summand of a Banach space need not be a topological direct summand. The main goal of this paper is to construct the theory of K$\small{\ddot{u}}$nneth type formula on bounded cohomology with real coefficients in the suitable category of Banach spaces with some restricted conditions.
Keywords
Bounded cohomology;K$\small{\ddot{u}}$nneth formula;
Language
English
Cited by
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