Proceedings of the International Conference on Geometry, Integrability and Quantization

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

Gregory Naber

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

Source
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

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


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