# 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 language English 80-109 30 Kodai Mathematical Journal 39 1 https://doi.org/10.2996/kmj/1458651693 Published - 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

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

Research output: Contribution to journalArticle

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