[100] Book Review: The Geometry and Physics of Knots by Michael Atiyah

Chapter

First Online: 27 March 2018

Part of the Contemporary Mathematicians book series (CM)

If a_k denotes the number of k-dimensional faces of a finite polyhedron P, then \(\chi (p) = \mathop \sum \nolimits {( - 1)^k}{a_k}\)

This is a preview of subscription content, to check access.

References

1. J. W. Alexander, Topoligical invariants of knots and links, Trans. Amer. Math. Soc. 30( 1928), 275.Google Scholar
2. R. Bott, Two new combinatorial invariants for polyhedra, Portugal. Math. 2 ( 1952), pp. 35-40.Google Scholar
3. S. Donaldson, An application of gauge theory to the topology of four manifolds, J. Differential Geom. 18 ( 1983), 269; Polynomial invariants for smooth four-manifolds, Oxford preprint.Google Scholar
4. R. MacPherson, The combinatorial formula of Gabrielov, Gelfand, and Losik for the first Pontrjagin class, Seminaire Bourbaki No. 497, Lecture Notes in Math., vol. 667, Berlin and New York, 1977.Google Scholar
5. L. Kaufman, State models and the Jones polynomial, Topology, 26 (1987), 395-407.Google Scholar
6. I. Lakatos, Proofs and refutations, Cambridge Univ. Press, London and New York, 1976.Google Scholar
7. V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer.Math. Soc. (N.S.) 12 (1985), 103-111.Google Scholar
8. E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989),351-399.Google Scholar