Celebratio Mathematica — Neumann — Complete Bibliography

Complete Bibliography

Works connected to Ted E. Petrie

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W. D. Neumann: “On the topology of curves in complex surfaces,” pp. 117–133 in Topological methods in algebraic transformation groups (New Brunswick, NJ, 4–8 April 1988). Edited by H. Kraft, T. Petrie, and G. W. Schwarz. Progress in Mathematics 80. Birkhäuser (Boston), 1989. MR 1040860 Zbl 0715.14025 incollection

We describe the use of the link at infinity as a tool to classify complex affine plane curves. This is an exposition of results of [Neumann 1989]. We give an overview of these results in §1, describe them precisely in §2, and give more examples in §4. §3 describes one of the topological ingredients: a substitute for the “Milnor fibration at infinity” when the latter does not exist.

The basic philosophy is that a three-manifold has a quite transparent structure given by its “toral decomposition,” and that for a three-manifold link of a complex analytic object this structure is induced from the structure in the complex object, and thus tells one a lot about it.

The same philosophy is useful also in other situations, and in §5 we make some remarks on links of divisors in surfaces, which we apply to show how the link at infinity of an affine homology plane determines the compactification divisor. This part of the paper is independent from the foregoing; it expands on a short digression in the conference talk.

Ted E. Petrie	Related
Gerald Walter Schwarz	Related