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Semigroups, d ‐invariants and deformations of cuspidal singular points of plane curves
Author(s) -
Borodzik Maciej,
Livingston Charles
Publication year - 2016
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdv068
Subject(s) - mathematics , gravitational singularity , constant (computer programming) , knot (papermaking) , singularity , torus , pure mathematics , deformation theory , singular point of a curve , plane curve , mathematical analysis , topology (electrical circuits) , geometry , combinatorics , computer science , chemical engineering , engineering , programming language
We study δ ‐constant deformations of plane curve singularities from a topological point of view. We introduce a topological counterpart to a δ ‐constant deformation in singularity theory. Methods from Heegaard Floer theory give a purely topological proof of the semicontinuity property for semigroups of singular points of plane curves under δ ‐constant deformation. Using the same approach, we also give a knot‐theoretical result concerning minimal unknotting sequences of torus knots. To conclude, we describe generalizations to arbitrary knots.