On certain complex surface singularities

  title={On certain complex surface singularities},
  author={Gergo Pint{\'e}r},
  journal={arXiv: Algebraic Topology},
  • Gergo Pintér
  • Published 29 April 2019
  • Mathematics
  • arXiv: Algebraic Topology
The thesis deals with holomorphic germs $ \Phi: (\mathbb{C}^2, 0) \to (\mathbb{C}^3,0) $ singular only at the origin, with a special emphasis on the distinguished class of finitely determined germs. The results are published in two articles (arXiv:1404.2853 and arXiv:1902.01229), joint with Andras Nemethi. In Chapter 3 of the thesis we study the associated immersion $ S^3 \looparrowright S^5 $, while Chapter 5 contains an algorithm providing the Milnor fibre boundary of the non-isolated… 

Figures from this paper

Cross-caps, triple points and a linking invariant for finitely determined germs

<jats:p>It was recently proved that for finitely determined germs <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \Phi : ( \mathbb C^2, 0) \rightarrow ( \mathbb C^3, 0)



The boundary of the Milnor fibre of certain non-isolated singularities

This paper provides the plumbing graph of the boundary of the Milnor fibre of f from the double-point-geometry of Phi, a finitely determined complex analytic germ.

Immersions associated with holomorphic germs

A holomorphic germ \Phi: (C^2, 0) \to (C^3, 0), singular only at the origin, induces at the links level an immersion of S^3 into S^5. The regular homotopy type of such immersions are determined by

The signature of smoothings of complex surface singularities

Let f : (1~3, 0)-"~(t~, 0) be the germ of a complex analytic function with an isolated critical point at the origin. For e > 0 suitably small and 6 yet smaller, the space V ' = f l ( 6 ) ~ D , (where

The boundary of the Milnor fiber of Hirzebruch surface singularities

We give the first (as far as we know) complete description of the boundary of the Milnor fiber for some non-isolated singular germs of surfaces in ${\bf C}^3$. We study irreducible (i.e. $gcd (m,k,l)

The boundary of the Milnor fibre of complex and real analytic non-isolated singularities

Let $$f$$f and $$g$$g be holomorphic function-germs vanishing at the origin of complex analytic germs of dimension three. Suppose that they have no common irreducible component and that the real

Isolated Singular Points on Complete Intersections

This monograph gives a coherent account of the theory of isolated singularities of complete intersections. One encounters such singularities often as the central fibres of analytic map-germs; that is

Three-Dimensional Link Theory and Invariants of Plane Curve Singularities.

This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction

Regular homotopy classes of immersions of 3-manifolds into 5-space

Abstract We give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifold into