Jacobian tori associated with a finite graph and its abelian covering graphs

Motoko Kotani; Toshikazu Sunada

doi:10.1006/aama.1999.0672

Jacobian tori associated with a finite graph and its abelian covering graphs

Motoko Kotani, Toshikazu Sunada

Leadership

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

We develop a graph-theoretic analogue of the Jacobian torus, which is defined, for a finite graph X, as the torus H¹(X,R)/H¹(X,Z) with a natural flat metric. It is observed that this notion, especially the volume of Jacobian tori, appears in many contexts of graph theory.

Original language	English
Pages (from-to)	89-110
Number of pages	22
Journal	Advances in Applied Mathematics
Volume	24
Issue number	2
DOIs	https://doi.org/10.1006/aama.1999.0672
Publication status	Published - 2000 Feb

Keywords

Jacobian torus; Albanese torus; abelian covering; complexity; girth

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1006/aama.1999.0672

Cite this

@article{73edf3acabad433b8f90b11ab847cce6,

title = "Jacobian tori associated with a finite graph and its abelian covering graphs",

abstract = "We develop a graph-theoretic analogue of the Jacobian torus, which is defined, for a finite graph X, as the torus H1(X,R)/H1(X,Z) with a natural flat metric. It is observed that this notion, especially the volume of Jacobian tori, appears in many contexts of graph theory.",

keywords = "Jacobian torus; Albanese torus; abelian covering; complexity; girth",

author = "Motoko Kotani and Toshikazu Sunada",

year = "2000",

month = feb,

doi = "10.1006/aama.1999.0672",

language = "English",

volume = "24",

pages = "89--110",

journal = "Advances in Applied Mathematics",

issn = "0196-8858",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Jacobian tori associated with a finite graph and its abelian covering graphs

AU - Kotani, Motoko

AU - Sunada, Toshikazu

PY - 2000/2

Y1 - 2000/2

N2 - We develop a graph-theoretic analogue of the Jacobian torus, which is defined, for a finite graph X, as the torus H1(X,R)/H1(X,Z) with a natural flat metric. It is observed that this notion, especially the volume of Jacobian tori, appears in many contexts of graph theory.

AB - We develop a graph-theoretic analogue of the Jacobian torus, which is defined, for a finite graph X, as the torus H1(X,R)/H1(X,Z) with a natural flat metric. It is observed that this notion, especially the volume of Jacobian tori, appears in many contexts of graph theory.

KW - Jacobian torus; Albanese torus; abelian covering; complexity; girth

UR - http://www.scopus.com/inward/record.url?scp=0038011738&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038011738&partnerID=8YFLogxK

U2 - 10.1006/aama.1999.0672

DO - 10.1006/aama.1999.0672

M3 - Article

AN - SCOPUS:0038011738

SN - 0196-8858

VL - 24

SP - 89

EP - 110

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 2

ER -

Jacobian tori associated with a finite graph and its abelian covering graphs

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this