Topological Lagrangians and cohomology

✍ Scribed by M.F. Atiyah; L. Jeffrey

• Book ID: 103906766
• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 703 KB
• Volume: 7
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/0393-0440(90)90023-v

✦ Synopsis

Witten [12] has interpreted the Donaldson invariants of four-manifolds by means of a topological Lagrangian. We show that this Lagrangian shouM be understood in terms of an infinite-dimensional analogue of the Gauss-Bonnet formula. Starting with a formula of Mathai and Quillen for the Thorn class, we obtain a formula for the Euler class of a vector bundle, which formally yields the explicit form of Witten's Lagrangian. We use the same method to treat Lagrangians proposed for the Casson invarian t.