Representation variety of free or surface groups and Reidemeister torsion

Hezenci, Fatih; SÖZEN, YAŞAR

doi:10.3906/mat-2110-25

Representation variety of free or surface groups and Reidemeister torsion

Hezenci F., SÖZEN Y.

TURKISH JOURNAL OF MATHEMATICS, vol.46, pp.1408-1423, 2022 (SCI-Expanded, Scopus, TRDizin)

Publication Type: Article / Article
Volume: 46
Publication Date: 2022
Doi Number: 10.3906/mat-2110-25
Journal Name: TURKISH JOURNAL OF MATHEMATICS
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
Page Numbers: pp.1408-1423
Keywords: Reidemeister torsion, representation varieties, Atiyah-Bott-Goldman symplectic form, symplectic chain complex, hyperbolic 3-manifolds, FUNDAMENTAL-GROUPS, ANALYTIC TORSION, R-TORSION, MODULI
Hacettepe University Affiliated: Yes

Abstract

For G is an element of {GL(n, C), SL(n, C)} , we consider G-valued representations of free or surface group with genus > 1. We establish a formula for computing Reidemeister torsion of such representations in terms of Atiyah-Bott-Goldman symplectic form for G. Furthermore, we apply the obtained results to hyperbolic 3-manifolds.