KIRCHHOFF'S THEOREMS IN HIGHER DIMENSIONS AND REIDEMEISTER TORSION

被引：11

作者：

Catanzaro, Michael J. ^{[1
]}

Chernyak, Vladimir Y. ^{[2
]}

Klein, John R. ^{[1
]}

机构：

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[2] Wayne State Univ, Dept Chem, Detroit, MI 48202 USA

来源：

HOMOLOGY HOMOTOPY AND APPLICATIONS | 2015年 / 17卷 / 01期

基金：

美国国家科学基金会;

关键词：

spanning tree; CW complex; Reidemeister torsion; combinatorial Laplacian; Kirchhoff's formulae; COMPLEXES; PROOF;

D O I：

10.4310/HHA.2015.v17.n1.a8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using, ideas from algebraic topology and statistical mechanics, we generalize Kirchhoff's network and matrix-tree theorems to finite CW complexes of arbitrary dimension. As an application, we give a formula expressing Reidemeister torsion as an enumeration of higher dimensional spanning trees.

引用

页码：165 / 189

页数：25

共 21 条

[1]

[Anonymous], 1998, GRADUATE TEXTS MATH

[2]

[Anonymous], 1970, CANADIAN MATH MONOGR

[3]

[Anonymous], 1923, REV MATEMATICA HISPA

[4]

[Anonymous], 1958, IRE T CIRCUIT THEORY

[5] A COMBINATORIAL PROOF OF THE ALL MINORS MATRIX TREE THEOREM [J].

CHAIKEN, S .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1982, 3 (03) :319-329

[6] Quantization and fractional quantization of currents in periodically driven stochastic systems. II. Full counting statistics [J].

Chernyak, Vladimir Y. ;

Klein, John R. ;

Sinitsyn, Nikolai A. .

JOURNAL OF CHEMICAL PHYSICS, 2012, 136 (15)

[7] Quantization and fractional quantization of currents in periodically driven stochastic systems. I. Average currents [J].

Chernyak, Vladimir Y. ;

Klein, John R. ;

Sinitsyn, Nikolai A. .

JOURNAL OF CHEMICAL PHYSICS, 2012, 136 (15)

[8]

Chernyak VladimirY., 2013, Advances in Mathematics, V244, P791

[9]

Duval A. M., J ALGEBRAIC IN PRESS

[10] Cellular spanning trees and Laplacians of cubical complexes [J].

Duval, Art M. ;

Klivans, Caroline J. ;

Martin, Jeremy L. .

ADVANCES IN APPLIED MATHEMATICS, 2011, 46 (1-4) :247-274

← 1 2 3 →