Exotic Heat PDE's.II

Details Exotic Heat PDE's.II Exotic Heat PDE's.II

2010-09-06

arxiv.org/abs/1009.1176v3

Mathematics

Algebraic Topology

43 pages, 8 figures

Scientific paper

Exotic heat equations that allow to prove the Poincar\'e conjecture and its generalizations to any dimension are considered. The methodology used is the PDE's algebraic topology, introduced by A. Pr\'astaro 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 {\em exotic spheres}, i.e., homotopy spheres that are homeomorphic, but not diffeomorphic to the standard $S^n$.

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