Algebraic knots associated with Milnor fibrations

Raimundo Araújo dos Santos, Osamu Saeki, and Taciana O. Souza

Journal of Singularities
volume 25 (2022), 30-53

Received: 31 January 2021. Received in revised form: 13 June 2022.

DOI: 10.5427/jsing.2022.25b

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Abstract:

In this paper, after reviewing basic material on Milnor fibrations, we explain topological invariants of algebraic knots associated with isolated singularities of complex hypersurfaces. These invariants have their origins in knot theory and are very important for the classification of isolated singularities of complex hypersurfaces up to certain topological equivalence relations. These relations correspond to isotopy and cobordism of associated knots. We also discuss the existence of non-trivial examples of real Milnor fibrations and the fibered knot conjecture.

2010 Mathematical Subject Classification:

Primary 32S55; Secondary 57Q45, 57M25

Key words and phrases:

Knot, Milnor fibration, topological invariant, knot cobordism

Author(s) information:

Raimundo Araújo dos Santos

Osamu Saeki

Taciana O. Souza