A new proof of the signature formula for surface bundles

✍ Scribed by Matthias Hoster

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 97 KB
• Volume: 112
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00233-3

✦ Synopsis

Let E → X be an oriented surface bundle over a closed surface. Then the signature sign(E) is determined by the first Chern class of the flat vector bundle Γ associated to the monodromy homomorphism χ :

. The aim of this paper is to give an algebro-topological proof of this formula, i.e., one that does not use the Atiyah-Singer index theorem.