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Abstract In this paper, we generalize the original idea of Thurston for the so-called Mather-Thurston’s theorem for foliated bundles to prove new variants of this theorem for PL homeomorphisms and contactormorphisms. These versions answer questions posed by Gelfand-Fuks ([GF73, Section 5]) and Greenberg ([Gre92]) on PL foliations and Rybicki ([Ryb10, Section 11]) on contactomorphisms. The interesting point about the original Thurston’s technique compared to the better-known Segal-McDuff’s proof of the Mather-Thurston theorem is that it gives acompactly supportedc-principle theorem without knowing the relevant local statement on open balls. In the appendix, we show that Thurston’s fragmentation implies the non-abelian Poincare duality theorem and its generalization using blob complexes ([MW12, Theorem 7.3.1]). To the memory of John Mather.
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Corrigendum to “Linear operators, the Hurwitz zeta function and Dirichlet L-functions” [J. Number Theory 217 (2020) 422–442]
We correct an error found in Section 3.4.1 of Linear operators, the Hurwitz zeta function and Dirichlet L-functions published in JNT 217 (2020) 422–442. The error is related to the convergence of the inverse operator G−1 defined in Section 3.3 and affects the statement and proof of Proposition 17. We provide a revised statement and proof.
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- Award ID(s):
- 2001909
- PAR ID:
- 10538646
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of Number Theory
- Volume:
- 234
- Issue:
- C
- ISSN:
- 0022-314X
- Page Range / eLocation ID:
- 499 to 502
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jnt.2021.07.013
