Smooth structures,normalized Ricci flows,and finite cyclic groups |
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Authors: | Masashi Ishida Ioana Şuvaina |
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Institution: | (1) Department of Mathematics, Sophia University, 7-1 Kioi-Cho, Chiyoda-Ku, Tokyo 102-8554, Japan;(2) IHES, 35 route de Chartres, 91440 Bures-sur-Yvette, France |
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Abstract: | A solution to the normalized Ricci flow is called non-singular if it exists for all time with uniformly bounded sectional
curvature. By using the techniques developed by the present authors Ishida, The normalized Ricci flow on four-manifolds and
exotic smooth structures; Şuvaina, Einstein metrics and smooth structures on non-simply connected 4-manifolds] we prove that
for any finite cyclic group , where d > 1, there exist infinitely many compact topological 4-manifolds, with fundamental group , which admit at least one smooth structure for which non-singular solutions of the normalized Ricci flow exist, but also
admit infinitely many distinct smooth structures for which no non-singular solution of the normalized Ricci flow exists. We show that there are no non-singular -equivariant, d > 1, solutions to the normalized Ricci flow on appropriate connected sums of and . |
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Keywords: | Normalized Ricci flows Exotic smooth structures Seiberg-Witten theory Finite cyclic fundamental groups |
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