TY - JOUR
T1 - The normalized ricci flow on four-manifolds and exotic smooth structures
AU - Ishida, Masashi
N1 - Publisher Copyright:
© 2016 International Press.
PY - 2016
Y1 - 2016
N2 - 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.
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.
KW - Exotic smooth structure
KW - Non-singular solution
KW - Ricci flow
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U2 - 10.4310/AJM.2016.v20.n5.a4
DO - 10.4310/AJM.2016.v20.n5.a4
M3 - Article
AN - SCOPUS:85015253578
VL - 20
SP - 903
EP - 918
JO - Asian Journal of Mathematics
JF - Asian Journal of Mathematics
SN - 1093-6106
IS - 5
ER -