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- W2037440724 abstract "We give a non-Abelian analogue of Whitney’s 2-isomorphism theorem for graphs. Whitney’s theorem states that the cycle space determines a graph up to 2-isomorphism. Instead of considering the cycle space of a graph which is an Abelian object, we consider a mildly non-Abelian object, the 2-truncation of the group algebra of the fundamental group of the graph considered as a subalgebra of the 2-truncation of the group algebra of the free group on the edges. The analogue of Whitney’s theorem is that this is a complete invariant of 2-edge connected graphs: let G, G′ be 2-edge connected finite graphs; if there is a bijective correspondence between the edges of G and G′ that induces equality on the 2-truncations of the group algebras of the fundamental groups, then G and G′ are isomorphic." @default.
- W2037440724 created "2016-06-24" @default.
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- W2037440724 date "2013-07-24" @default.
- W2037440724 modified "2023-09-23" @default.
- W2037440724 title "A non-Abelian analogue of Whitney’s 2-isomorphism theorem" @default.
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- W2037440724 doi "https://doi.org/10.1007/s10801-013-0461-x" @default.
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