An exotic smooth structure on CP^2+6CP^2-bar
We construct smooth 4-manifolds homeomorphic but not diffeomorphic to CP^2+6CP^2-bar.
math.GT↗
arXiv subjects
Andras I Stipsicz
Publications and source records attributed to Andras I Stipsicz.
Exotic smooth structures on $CP^2#5{\bar CP^2}$
Motivated by a construction of Fintushel and Stern, we show that the topological 4--manifold $CP^2#5{\bar CP^2}$ supports infinitely many distinct smooth structures.
math.GT↗
Small Exotic 4-manifolds with b_2^+=3
We construct an infinite family of simply connected, pairwise nondiffeomorphic 4-manifolds, all homeomorphic to 3CP^2 blown up at 9 points.
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Ozsvath-Szabo invariants and tight contact three-manifolds, I
Let S^3_r(K) be the oriented 3--manifold obtained by rational r-surgery on a knot K in S^3. Using the contact Ozsvath-Szabo invariants we prove, for a class of knots K containing all the algebraic knots, that S^3_r(K) carries positive, tight contact structures for every r not= 2g_s(K)-1, where g_s(K) is the slice genus of K. This implies, in particular, that the Brieskorn spheres -Sigma(2,3,4) and -Sigma(2,3,3) carry tight, positive contact structures. As an application of our main result we show that for each m in N there exists a Seifert fibered rational homology 3-sphere M_m carrying at least m pairwise non-isomorphic tight, nonfillable contact structures.
math.SG↗
An infinite family of tight, not semi-fillable contact three-manifolds
We prove that an infinite family of virtually overtwisted tight contact structures discovered by Honda on certain circle bundles over surfaces admit no symplectic semi-fillings. The argument uses results of Mrowka, Ozsvath and Yu on the translation-invariant solutions to the Seiberg-Witten equations on cylinders and the non-triviality of the Kronheimer-Mrowka monopole invariants of symplectic fillings.
math.SG↗