A Note on Representation Variety of Abelian Groups and Reidemeister Torsion
Küçük Resim Yok
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Let S and G denote respectively the 2 - torus and one of the Lie groups GL (n, C), SL (n, C), SO (n, C), Sp (2 n, C). In the present article, we consider the smooth part of the representation variety Rep (S, G) consisting of conjugacy classes of homomorphisms from fundamental group ?1(S) to G. We show the well definiteness of Reidemeister torsion for such representations. In addition, we establish a formula for computing the Reidemeister torsion of such representations in terms of the symplectic structure on Rep (S, G) [51]. This symplectic form is analogous to Atiyah–Bott–Goldman symplectic form of higher genera for the Lie group G. © 2021, Springer Nature Switzerland AG.
Açıklama
4th International Conference on Analysis and Applied Mathematics, ICAAM 2018 -- 6 September 2018 through 9 September 2018 -- -- 262329
Anahtar Kelimeler
Abelian varieties, Atiyah-Bott-Goldman Symplectic Form, Chain complex, Reidemeister torsion, Representation varieties, Symplectic chain complex
Kaynak
Springer Proceedings in Mathematics and Statistics
WoS Q Değeri
Scopus Q Değeri
N/A
Cilt
351
