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In this article we construct a minimal symplectic –manifold and prove it is homeomorphic but not diffeomorphic to .
Baldridge, Scott 1 ; Kirk, Paul A 2
@article{GT_2008_12_2_a4, author = {Baldridge, Scott and Kirk, Paul A}, title = {A symplectic manifold homeomorphic but not diffeomorphic to {CP2#3CP2}}, journal = {Geometry & topology}, pages = {919--940}, publisher = {mathdoc}, volume = {12}, number = {2}, year = {2008}, doi = {10.2140/gt.2008.12.919}, url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2008.12.919/} }
TY - JOUR AU - Baldridge, Scott AU - Kirk, Paul A TI - A symplectic manifold homeomorphic but not diffeomorphic to CP2#3CP2 JO - Geometry & topology PY - 2008 SP - 919 EP - 940 VL - 12 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/gt.2008.12.919/ DO - 10.2140/gt.2008.12.919 ID - GT_2008_12_2_a4 ER -
Baldridge, Scott; Kirk, Paul A. A symplectic manifold homeomorphic but not diffeomorphic to CP2#3CP2. Geometry & topology, Tome 12 (2008) no. 2, pp. 919-940. doi : 10.2140/gt.2008.12.919. http://geodesic.mathdoc.fr/articles/10.2140/gt.2008.12.919/
[1] Exotic smooth structures on $3\mathbb{CP}^2\#7\overline{\mathbb{CP}}^2$
,[2] Exotic smooth structures on small $4$–manifolds
, ,[3] Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves, Math. Ann. 326 (2003) 185
, , ,[4] New symplectic 4-manifolds with $b_+=1$, Math. Ann. 333 (2005) 633
,[5] Luttinger surgery and interesting symplectic 4-manifolds with small Euler characteristic,
, ,[6] Symplectic 4-manifolds with arbitrary fundamental group near the Bogomolov-Miyaoka-Yau line, J. Symplectic Geom. 4 (2006) 63
, ,[7] On symplectic 4-manifolds with prescribed fundamental group, Comment. Math. Helv. 82 (2007) 845
, ,[8] Irrationality and the $h$–cobordism conjecture, J. Differential Geom. 26 (1987) 141
,[9] Families of simply connected $4$–manifolds with the same Seiberg–Witten invariants, Topology 43 (2004) 1449
, ,[10] Double node neighborhoods and families of simply connected $4$–manifolds with $b^+=1$, J. Amer. Math. Soc. 19 (2006) 171
, ,[11] The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357
,[12] A new construction of symplectic manifolds, Ann. of Math. $(2)$ 142 (1995) 527
,[13] On manifolds homeomorphic to $\mathbb{CP}^2\# 8\overline{\mathbb{CP}}^2$, Invent. Math. 95 (1989) 591
,[14] Lagrangian tori in $\mathbb{R}^4$, J. Differential Geom. 42 (1995) 220
,[15] Introduction to symplectic topology, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press (1998)
, ,[16] On Park's exotic smooth four-manifolds, from: "Geometry and topology of manifolds", Fields Inst. Commun. 47, Amer. Math. Soc. (2005) 253
, ,[17] Simply connected symplectic $4$–manifolds with $b^+_2=1$ and $c^2_1=2$, Invent. Math. 159 (2005) 657
,[18] Exotic smooth structures on $\mathbb{CP}^2\#5\overline{\mathbb{CP}^2}$, Math. Res. Lett. 12 (2005) 701
, , ,[19] An exotic smooth structure on $\mathbb C\mathbb P^2\#6\overline\mathbb{C\mathbb P^2}$, Geom. Topol. 9 (2005) 813
, ,[20] Counting pseudo-holomorphic submanifolds in dimension $4$, J. Differential Geom. 44 (1996) 818
,[21] Seiberg–Witten and Gromov invariants, from: "Geometry and physics (Aarhus, 1995)", Lecture Notes in Pure and Appl. Math. 184, Dekker (1997) 591
,[22] Minimality and symplectic sums, Int. Math. Res. Not. (2006) 17
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