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  • On the theorems of Sard and de Rham

    Creator:
    Short, Donald Ray
    Abstract:
    A geometric condition on differentiable maps is given which is equivalent to the set of critical values being nowhere dense. In particular, the geometric condition is satisfied for radially ductile maps. On the other hand it is proved that the induced map on the de Rham complex will be a...
    Resource Type:
    Dissertation

  • On the Topologies of Moduli Spaces of Polygons: A Taxonomic Approach

    Creator:
    Krughoff, Stephen A.
    Abstract:
    Consider a polygon lying in the Euclidean plane with labeled edge lengths. The moduli space of polygons is the space of all polygons with the same labeled edge lengths, modulo orientation preserving isometries. It is well known that this space is generically a smooth manifold. For certain combinations of edge...
    Resource Type:
    Dissertation
    Full Text:
    topology and geometry, and for the freedom to pursue my own path through my graduate career. • to the