Additivity of the rho map on the topological structure group

Paolo Piazza; Vito Felice Zenobi

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arXiv · 1607.07075

Additivity of the rho map on the topological structure group

Paolo Piazza·Vito Felice Zenobi

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Abstract

Let M be an orientable topological manifold of dimension m, m greater or equal to 5, with fundamental group $\Gamma$. Let S(M) be the topological structure set, endowed with the group structure induced by its identification with Ranicki's algebraic structure set. We prove that the (rationalized) rho map $\rho_\Gamma: S(M)\rightarrow K_{m+1} (D^*_\Gamma)\otimes \mathbb{Q}$ is a homomorphism of abelian groups.

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Paolo Piazza, Vito Felice Zenobi. 2016-07-24. Additivity of the rho map on the topological structure group. https://arxiv.org/abs/1607.07075

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