Corpus ID: 119284185

Sheaves, Cosheaves and Applications

@article{Curry2014SheavesCA,
  title={Sheaves, Cosheaves and Applications},
  author={J. Curry},
  journal={arXiv: Algebraic Topology},
  year={2014}
}
  • J. Curry
  • Published 2014
  • Mathematics
  • arXiv: Algebraic Topology
  • This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science and engineering. To provide a theory that is computable, we focus on a combinatorial version of sheaves and cosheaves called cellular sheaves and cosheaves, which are finite families of vector spaces and maps parametrized by a cell complex. We develop cellular (co)sheaves as a new tool for topological data analysis, network coding and sensor networks. A foundation for multi-dimensional level-set… CONTINUE READING
    Dualities between Cellular Sheaves and Cosheaves
    6
    Sheaf-Theoretic Stratification Learning
    6
    Classification of Constructible Cosheaves
    13
    Toward a spectral theory of cellular sheaves
    11
    Persistent homology and microlocal sheaf theory
    33
    Modules over posets: commutative and homological algebra
    A Sheaf-Theoretic Perspective on Sampling
    6

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