Branched Polymers and Hyperplane Arrangements

被引：1

作者：

Meszaros, Karola ^{[1
]}

Postnikov, Alexander ^{[2
]}

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

[2] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2013年 / 50卷 / 01期

基金：

美国国家科学基金会;

关键词：

Polymers; Braid arrangement; Hyperplane arrangement; Characteristic polynomial; Broken circuit; Orlik-Solomon algebra;

D O I：

10.1007/s00454-013-9499-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie (Ann Math, 158:1019-1039, 2003), and Kenyon and Winkler (Am Math Mon, 116(7):612-628, 2009) to any central hyperplane arrangement . The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement is expressed through the value of the characteristic polynomial of at 0. We give a more general definition of the space of branched polymers, where we do not require connectivity, and introduce the notion of q-volume for it, which is expressed through the value of the characteristic polynomial of at . Finally, we relate the volume of the space of branched polymers to broken circuits and show that the cohomology ring of the space of branched polymers is isomorphic to the Orlik-Solomon algebra.

引用

页码：22 / 38

页数：17

共 5 条

[1]

[Anonymous], 2013, Modern graph theory

[2] Branched polymers and dimensional reduction [J].