## Proceedings of the International Conference on Geometry, Integrability and Quantization

- Geom. Integrability & Quantization
- Proceedings of the Third International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Gregory L. Naber, eds. (Sofia: Coral Press Scientific Publishing, 2002), 105 - 140

### Invariants of Smooth Four-Manifolds: Topology, Geometry, Physics

#### Abstract

The profound and beautiful interaction between smooth four-manifold topology and the quantum theory of fields often seems as impenetrable as it is impressive. The objective of this series of lectures is to provide a very modest introduction to this interaction by describing, in terms as elementary as possible, how Atiyah and Jeffrey [1] came to view the partition function of Witten’s first topological quantum field theory [21], which coincides with the zero-dimensional Donaldson invariant, as an “Euler characteristic” for an infinite-dimensional vector bundle.

#### Article information

**Dates**

First available in Project Euclid:
12 June 2015

**Permanent link to this document**

https://projecteuclid.org/
euclid.pgiq/1434145463

**Digital Object Identifier**

doi:10.7546/giq-3-2002-64-104

**Mathematical Reviews number (MathSciNet)**

MR1884841

**Zentralblatt MATH identifier**

1008.57025

#### Citation

Naber, Gregory. Invariants of Smooth Four-Manifolds: Topology, Geometry, Physics. Proceedings of the Third International Conference on Geometry, Integrability and Quantization, 105--140, Coral Press Scientific Publishing, Sofia, Bulgaria, 2002. doi:10.7546/giq-3-2002-64-104. https://projecteuclid.org/euclid.pgiq/1434145463

Copyright © Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences