Some Open Problems in the Theory of Singularities of Mappings
David Mond · Journal of Singularities · 2015
This paper surveys some open problems in the theory of singularities of mappings. It does not claim to be comprehensive or fair. The problems are those whose answers I would most like to see. 1. Vanishing homology of parameterisations of hypersurfaces 1.1. versus . Germs of mappings fromn-space to n+1-space show some of the same features as isolated complete intersection singularities. I'm thinking in particular of the relation between the rank of the vanishing homology ( ) and theAe{codimension ( ). This relation, which I will describe in detail in a moment, can be seen already in the three Reidemeister moves of knot theory. The three moves are those unavoidably present when we deform one plane knot diagram to another.