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Exotic Heat PDE’s.II

In: Essays in Mathematics and its Applications

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  • Agostino Prástaro

    (University of Roma “La Sapienza”, Department SBAI, Mathematics (ex MEMOMAT))

Abstract

Exotic heat equations that allow to prove the Poincaré conjecture and its generalizations to any dimension are considered. The methodology used is the PDE’s algebraic topology, introduced by A. Prástaro in the geometry of PDE’s, in order to characterize global solutions. In particular it is shown that this theory allows us to identify n-dimensional exotic spheres, i.e., homotopy spheres that are homeomorphic, but not diffeomorphic to the standard $${S}^{n}$$ .

Suggested Citation

  • Agostino Prástaro, 2012. "Exotic Heat PDE’s.II," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Essays in Mathematics and its Applications, edition 127, pages 369-419, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-28821-0_15
    DOI: 10.1007/978-3-642-28821-0_15
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