Background Reading and References

Normal Surfaces and Decision Problems in 3-Manifolds

August 5-9, 1996

University of California, Davis

Main Speaker

J. Hyam Rubinstein (Melbourne University)

Background Reading and References

Normal Surfaces:

1. Haken, W. ``Theorie der Normalflachen'', Acta. Math. Vol. 105, 1961, pp. 245-375.
2. Jaco, W., ``Lectures on three-manifold topology'', A.M.S., Regional conference series in math, no. 43, 1980.
3. Jaco, W. and Oertel, U., ``An Algorithm to Decide if a 3-Manifold is a Haken Manifold'', Topology Vol. 23, No. 2, 1984, pp. 195-209.
4. Jaco, W. and Rubinstein, J.H., ``A piecewise linear theory of minimal surfaces in 3-manifolds'', J. Diff. Geom. Vol. 27, 1988, pp. 493-524.
5. Hemion, G., `The Classification of Knots and 3-dimensional Spaces'', Oxford University Press, 1992.

Minimal Surfaces:

1. W. Jaco and J. H. Rubinstein, PL equivariant surgery and invariant decompositions of 3-manifolds, Advances in Math 73 (1989) 149-191.
2. 2. W. Jaco and J. H. Rubinstein, PL minimal surfaces in 3-manifolds, J. Differential Geometry 27 (1988). 493-524.
3. J. Pitts and J. H. Rubinstein, Equivariant minimax and minimal surfaces in geometric 3-manifolds, Bull. American Math. Soc. 19 (1988) 303-309.

The Space Form Problem:

Almost normal surfaces:

1. J. H. Rubinstein, Polyhedral minimal surfaces, ,eegaard splittings and decision problems for 3-dimensional manifolds, to appear in Proceedings of the Georgia Topology Conference, 1993.
2. J. H. Rubinstein, An algorithm to recognize the 3-sphere, to appear in Proceedings of the ICM, Zurich 1994.
3. Thompson, A., ``Thin Position and the Recognition Problem for $S^3$'', {\it Math. Research Letter} 1, 1994, pp.613-630.
4. Matveev, S. V., ``The J.H. Rubinstein - A. Thompson algorithm for the recognition of $S^3$''

Heegaard Splittings:

1. J. H. Rubinstein and M. Scharlemann, Comparing Heegaard splitting of 3-manifolds, submitted to Topology.

Cubings:

1. I. Aitchison and J. H. Rubinstein, An introduction to polyhedral metrics of non-positive curvature, in Geometry of Low-dimensional manifolds, Vol II, 27-71, Cambridge University Press, 1990.
2. I. Aitchison, E. Lumsden and J. H. Rubinstein, Cusp structures of alternating links, Inventiones Math 109 (1992) 473-494.

11-22-95

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