A generic classification of function germs with respect to the reticular \(t-{\mathcal P}-{\mathcal K}\)-equivalence (Q1026998)

By extending a notion by \textit{S. Izumiya} [J. Differ. Geom. 38, No. 3, 485--500 (1993; Zbl 0781.57016)], the author introduces a general equivalence relation called ``reticular \(t\)-\({\mathcal P}\)-\({\mathcal K}\)-equivalence'' of function germs in \({\mathfrak M}(r; k+ n+ m)\) and gives a generic classification in the case \(r= 0\), \(n\leq 5\), \(m\leq 1\) and \(r= 1\), \(n\leq 3\), \(m\leq 1\), respectively. As it is expected, this work will play an important role in a generic classification of bifurcations of wave fronts generaetd by a hypersurface germ with a boundary (T. Tsukuda, in preparation).