Virtual hodge polynomials of the moduli spaces of representations of degree 2 for free monoids

Kazunori Nakamoto, Takeshi Torii

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper we study the topology of the moduli spaces of representations of degree 2 for free monoids. We calculate the virtual Hodge polynomials of the character varieties for several types of 2-dimensional representations. Furthermore, we count the number of isomorphism classes for each type of 2-dimensional representations over any finite field Fq, and show that the number coincides with the virtual Hodge polynomial evaluated at q.

Original languageEnglish
Pages (from-to)80-109
Number of pages30
JournalKodai Mathematical Journal
Volume39
Issue number1
DOIs
Publication statusPublished - Mar 25 2016

Fingerprint

Monoids
Moduli Space
Character Variety
Polynomial
Isomorphism Classes
Galois field
Count
Topology
Calculate

Keywords

  • Character variety
  • Moduli of representations
  • Representation variety
  • Virtual hodge polynomial

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Virtual hodge polynomials of the moduli spaces of representations of degree 2 for free monoids. / Nakamoto, Kazunori; Torii, Takeshi.

In: Kodai Mathematical Journal, Vol. 39, No. 1, 25.03.2016, p. 80-109.

Research output: Contribution to journalArticle

@article{3e20e5ed07a248c4b55a8ecd5560561c,
title = "Virtual hodge polynomials of the moduli spaces of representations of degree 2 for free monoids",
abstract = "In this paper we study the topology of the moduli spaces of representations of degree 2 for free monoids. We calculate the virtual Hodge polynomials of the character varieties for several types of 2-dimensional representations. Furthermore, we count the number of isomorphism classes for each type of 2-dimensional representations over any finite field Fq, and show that the number coincides with the virtual Hodge polynomial evaluated at q.",
keywords = "Character variety, Moduli of representations, Representation variety, Virtual hodge polynomial",
author = "Kazunori Nakamoto and Takeshi Torii",
year = "2016",
month = "3",
day = "25",
doi = "10.2996/kmj/1458651693",
language = "English",
volume = "39",
pages = "80--109",
journal = "Kodai Mathematical Journal",
issn = "0386-5991",
publisher = "Tokyo Institute of Technology",
number = "1",

}

TY - JOUR

T1 - Virtual hodge polynomials of the moduli spaces of representations of degree 2 for free monoids

AU - Nakamoto, Kazunori

AU - Torii, Takeshi

PY - 2016/3/25

Y1 - 2016/3/25

N2 - In this paper we study the topology of the moduli spaces of representations of degree 2 for free monoids. We calculate the virtual Hodge polynomials of the character varieties for several types of 2-dimensional representations. Furthermore, we count the number of isomorphism classes for each type of 2-dimensional representations over any finite field Fq, and show that the number coincides with the virtual Hodge polynomial evaluated at q.

AB - In this paper we study the topology of the moduli spaces of representations of degree 2 for free monoids. We calculate the virtual Hodge polynomials of the character varieties for several types of 2-dimensional representations. Furthermore, we count the number of isomorphism classes for each type of 2-dimensional representations over any finite field Fq, and show that the number coincides with the virtual Hodge polynomial evaluated at q.

KW - Character variety

KW - Moduli of representations

KW - Representation variety

KW - Virtual hodge polynomial

UR - http://www.scopus.com/inward/record.url?scp=84961639801&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961639801&partnerID=8YFLogxK

U2 - 10.2996/kmj/1458651693

DO - 10.2996/kmj/1458651693

M3 - Article

VL - 39

SP - 80

EP - 109

JO - Kodai Mathematical Journal

JF - Kodai Mathematical Journal

SN - 0386-5991

IS - 1

ER -