科研之友
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摘要
We associate with any compact semi-algebraic set X subset of R-n chain complex of currents S-* (X) generated by integration along semi algebraic submanifolds, and we analyze the corresponding homology groups. In particular, we show that these homology groups satisfy the Eilenberg-Steenrod axioms, and further, that they are isomorphic to both the ordinary singular homology groups of X and to the homology groups generated by the integral currents supported on X. Using this result and a certain neighborhood of X, we are able to prove homological mass minimization for integral currents supported on X, and verify that any cycle of X that has sufficiently small mass is a boundary.
- 出版日期2016
