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, cilt.46, ss.1408-1423, 2022 (SCI-Expanded, Scopus, TRDizin)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 46
Basım Tarihi: 2022
Doi Numarası: 10.3906/mat-2110-25
Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
Sayfa Sayıları: ss.1408-1423
Anahtar Kelimeler: Reidemeister torsion, representation varieties, Atiyah-Bott-Goldman symplectic form, symplectic chain complex, hyperbolic 3-manifolds, FUNDAMENTAL-GROUPS, ANALYTIC TORSION, R-TORSION, MODULI
Hacettepe Üniversitesi Adresli: Evet

Özet

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.