Surgical Ricci flow on four-manifolds with positive isotropic curvature

2008 ◽  
pp. 101-109
Keyword(s):  
Ricci Flow ◽  
Isotropic Curvature ◽  
Four Manifolds

Four-manifolds with positive isotropic curvature

2016 ◽  
Vol 11 (5) ◽  
pp. 1123-1149
Author(s):  
Bing-Long Chen ◽  
Xian-Tao Huang
Keyword(s):  
Isotropic Curvature ◽  
Four Manifolds

NORMALIZED RICCI FLOW, SURGERY, AND SEIBERG–WITTEN INVARIANTS

2014 ◽  
Vol 25 (02) ◽  
pp. 1450005
Author(s):  
MASASHI ISHIDA
Keyword(s):  
Existence Theorem ◽  
Euler Characteristic ◽  
Ricci Flow ◽  
Einstein Metrics ◽  
Nonsingular Solution ◽  
Ricci Flows ◽  
Normalized Ricci Flow ◽  
Four Manifolds ◽  
Special Case

We investigate the behavior of solutions of the normalized Ricci flow under surgeries of four-manifolds along circles by using Seiberg–Witten invariants. As a by-product, we prove that any pair (α, β) of integers satisfying α + β ≡ 0 (mod 2) can be realized as the Euler characteristic χ and signature τ of infinitely many closed smooth 4-manifolds with negative Perelman's [Formula: see text] invariants and on which there is no nonsingular solution to the normalized Ricci flows for any initial metric. In particular, this includes the existence theorem of non-Einstein 4-manifolds due to Sambusetti [An obstruction to the existence of Einstein metrics on 4-manifolds, Math. Ann.311 (1998) 533–547] as a special case.

scholarly journals Isotropic Curvature and the Ricci Flow

2009 ◽  
Vol 2010 (3) ◽  
pp. 536-558 ◽  
Author(s):  
Huy T. Nguyen
Keyword(s):  
Ricci Flow ◽  
Isotropic Curvature
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