The normalized ricci flow on four-manifolds and exotic smooth structures

Masashi Ishida

doi:10.4310/AJM.2016.v20.n5.a4

The normalized ricci flow on four-manifolds and exotic smooth structures

Masashi Ishida

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We shall prove that, for every natural number I there exists a closed topological 4-manifold X_ℓ which admits smooth structures for which non-singular solutions of the normalized Ricci flow exist, but also admits smooth structures for which no non-singular solution of the normalized Ricci flow exists. Hence, in dimension 4, smooth structures become definite obstructions to the existence of non-singular solutions to the normalized Ricci flow.

Original language	English
Pages (from-to)	903-918
Number of pages	16
Journal	Asian Journal of Mathematics
Volume	20
Issue number	5
DOIs	https://doi.org/10.4310/AJM.2016.v20.n5.a4
Publication status	Published - 2016

Keywords

Exotic smooth structure
Non-singular solution
Ricci flow

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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AB - We shall prove that, for every natural number I there exists a closed topological 4-manifold Xℓ which admits smooth structures for which non-singular solutions of the normalized Ricci flow exist, but also admits smooth structures for which no non-singular solution of the normalized Ricci flow exists. Hence, in dimension 4, smooth structures become definite obstructions to the existence of non-singular solutions to the normalized Ricci flow.

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