Exotic PDE's

Details Exotic PDE's Exotic PDE's

2010-12-31

arxiv.org/abs/1101.0283v2

Mathematics

Algebraic Topology

51 pages, 1 figure

Scientific paper

In the framework of the PDE's algebraic topology, previously introduced by A. Pr\'astaro, are considered {\em exotic differential equations}, i.e., differential equations admitting Cauchy manifolds $N$ identifiable with exotic spheres, or such that their boundaries $\partial N$ are exotic spheres. For such equations are obtained local and global existence theorems and stability theorems. In particular the smooth ($4$-dimensional) Poincar\'e conjecture is proved. This allows to complete the previous Theorem 4.59 in \cite{PRA17} also for the case $n=4$.

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