Celebratio Mathematica — Neumann — Complete Bibliography

Complete Bibliography

Works connected to Jun Yang

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W. D. Neumann and J. Yang: “Invariants from triangulations of hyperbolic 3-manifolds,” Electron. Res. Announc. Am. Math. Soc. 1 : 2 (1995), pp. 72–79. MR 1350682 Zbl 0851.57013 article

W. D. Neumann and J. Yang: “Rationality problems for $K$ -theory and Chern–Simons invariants of hyperbolic 3-manifolds,” Enseign. Math. (2) 41 : 3–4 (1995), pp. 281–296. MR 1365848 Zbl 0861.57022 article

W. D. Neumann and J. Yang: Rationality problems for Chern–Simons invariants. Preprint, December 1997. ArXiv math/9712225 techreport

W. D. Neumann and J. Yang: “Bloch invariants of hyperbolic 3-manifolds,” Duke Math. J. 96 : 1 (1999), pp. 29–59. MR 1663915 Zbl 0943.57008 ArXiv math/9712224 article

We define an invariant $ \beta(M) $ of a finite volume hyperbolic 3-manifold $ M $ in the Bloch group $ \mathscr{B}(\mathbb{C}) $ and show it is determined by the simplex parameters of any degree one ideal triangulation of $ M $. We show $ \beta(M) $ lies in a subgroup of $ \mathscr{B}(\mathbb{C}) $ of finite $ \mathbb{Q} $-rank determined by the invariant trace field of $ M $. Moreover, the Chern–Simons invariant of $ M $ is determined modulo rationals by $ \beta(M) $. This leads to a simplicial formula and rationality results for the Chern–Simons invariant which appear elsewhere.

Generalizations of $ \beta(M) $ are also described, as well as several interesting examples. An appendix describes a scissors congruence interpretation of $ \mathscr{B}(\mathbb{C}) $.

W. D. Neumann and J. Yang: $μ$ -constancy does not imply constant bi-Lipschitz type. Preprint, September 2008. ArXiv 0809.0845 techreport