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- W4386813113 abstract "We investigate the following question: if A and A′ are products of finite cyclic groups, when does there exist an isomorphism f:A→A′ which preserves the union of coordinate hyperplanes (equivalently, so that f(x) has some coordinate zero if and only if x has some coordinate zero)? We show that if such an isomorphism exists, then A and A′ have the same cyclic factors; if all cyclic factors have order larger than 2, the map f is diagonal up to permutation, hence sends coordinate hyperplanes to coordinate hyperplanes. As a model application, we show using twisted signatures that there exists a family of compact 4-manifolds X(n) with H1X(n)=Z/n with the property that ∏X(ni)≅∏X(nj′) if and only if the factors may be identified (up to permutation), and that the induced map on first homology is represented by a diagonal matrix." @default.
- W4386813113 created "2023-09-18" @default.
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- W4386813113 date "2023-11-01" @default.
- W4386813113 modified "2023-10-07" @default.
- W4386813113 title "Hyperplanes in abelian groups and twisted signatures" @default.
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- W4386813113 doi "https://doi.org/10.1016/j.topol.2023.108692" @default.
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