Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers-Reference-Cited by-同舟云学术

Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers

Published:2017-11-23 Issue:18 Volume:2019 Page:5674-5702
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Chung Hee-Joong¹²,Kim Dohyeong³,Kim Minhyong²⁴,Pappas Georgios⁵,Park Jeehoon⁶,Yoo Hwajong⁷

Affiliation:

1. Department of Physics, Pohang University of Science and Technology, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk, Republic of Korea

2. Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Republic of Korea

3. Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043, USA

4. Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK

5. Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

6. Department of Mathematics, Pohang University of Science and Technology, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 37673, Republic of Korea

7. IBS Center for Geometry and Physics, Mathematical Science Building, Room 108, Pohang University of Science and Technology, 77 Cheongam-Korea, Nam-gu, Pohang, Gyeongbuk 37673, Republic of Korea

Abstract

AbstractFollowing the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of $n$-th power residue symbols. This formalism leads to a precise arithmetic analogue of a “path-integral formula” for linking numbers.

Funder

EPSRC

NSF

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2019/18/5674/30009323/rnx271.pdf

Reference16 articles.

1. Topological Methods in Hydrodynamics

2. “Unramified arithmetic Chern-Simons invariants.”;Bleher