We begin with a quick summary of the notions of global singularity theory and the theory of Thom polynomials. For a more detailed review we refer the reader to [1, 15]. Let N and K be two complex manifolds of dimensions n and k respectively; assume that n ≤ k. Consider a holomorphic map f : N → K for which the differential d fp : TpN → TpK at a generic point p ∈ N is nonsingular, i.e. has rank ...

The paper " Une théorie dynamique de la morphgenèse " , written by René Thom in 1966 and appeared in 1967 in Towards a theoretical Biology I, published by Conrad Hal Waddington, can be considered as the princeps paper of the catastrophe theory. In this paper Thom declares that embryology and, in particular, Waddington's notions of epigenetic landscape and chreod have been one of his sources in ...

An oriented connected closed manifold Mn is called a URC-manifold if for any oriented connected closed manifold Nn of the same dimension there exists a non-zero degree mapping of a finite-fold covering M̂n of Mn onto Nn. This condition is equivalent to the following: For any n-dimensional integral homology class of any topological space X , a multiple of it can be realized as the image of the fu...

Mathematical biology occupies a special place at the interface between the physical, mathematical and life sciences. Is this interface merely a meeting point for dabblers venturing out of their own proper domains to work on problems of mutual interest? Or is it an incipient science in its own right, with its own particular character, principles, and practices? The past century has seen vast adv...

Given the classification of low dimensional manifolds up to equivalence relations such as diffeomorphism or homeomorphism, one would hope to be able to continue to classify higher dimensional manifolds. Unfortunately, this turns out to be difficult or impossible, and so one solution would be turn to some weaker equivalence relation. One such equivalence relation would be to consider manifolds u...