Lefschetz Fibrations and an Invariant of Finitely Presented Groups
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, sa.9, ss.1547-1572, 2009 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2009
- Doi Numarası: 10.1093/imrn/rnn164
- Dergi Adı: INTERNATIONAL MATHEMATICS RESEARCH NOTICES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1547-1572
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
Every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. This follows from results of Gompf and Donaldson, and was also proved by Amoros-Bogomolov-Katzarkov-Pantev. We give another proof by providing the monodromy explicitly. We then define the genus of a finitely presented group Gamma to be the minimal genus of a Lefschetz fibration with fundamental group Gamma. We also give some estimates of the genus of certain groups.