Functor calculus and the discriminant method (Q2922464)

The authors reformulate the discriminant method in the language of functor calculus. This reformulation permits to use the discriminant method in a setting where some conditions on the multilocal behavior of smooth maps \(f :L \rightarrow \mathbb{R}^k\) are imposed. The paper is organized into four sections dealing with the following topics: the discriminant method after Vassiliev, discriminant method and manifold calculus, admissible multijets. At the end of the paper five appendices completing the material are given: interpolation and tameness; topology of badness; excision in locally finite homology; boundary conditions; polynomial functors, analytic functors and duality. Another paper by the authors directly connected to this subject is [\textit{R. Reis} and \textit{M. S. Weiss}, Port. Math. (N.S.) 69, No. 1, 41--67 (2012; Zbl 1266.58022)], and by the second author there are [\textit{T. G. Goodwillie} and \textit{M. Weiss}, Geom. Topol. 3, 103--118 (1999; Zbl 0927.57028)] (with T. G. Goodwillie), [\textit{M. Weiss}, Bull. Am. Math. Soc., New Ser. 33, No. 2, 177--187 (1996; Zbl 0870.57042), Geom. Topol. 3, 67--101 (1999; Zbl 0927.57027); erratum ibid. 15, No. 1, 407--409 (2011)] and [Q. J. Math. 55, No. 4, 499--504 (2004; Zbl 1065.57030)].