Rational homology balls in 2-handlebodies. (English) Zbl 1420.57075
Summary: We prove that there are rational homology balls \(B_p\) smoothly embedded in the \(2\)-handlebodies associated to certain knots. Furthermore we show that, if we rationally blow up the \(2\)-handlebody along the embedded rational homology ball \(B_p\), then the resulting \(4\)-manifold cannot be obtained just by a sequence of ordinary blow ups from the \(2\)-handlebody under a certain mild condition.
MSC:
| 57R40 | Embeddings in differential topology |
| 57R55 | Differentiable structures in differential topology |
References:
| [1] | S. Akbulut and K. Yasui, Corks, plugs and exotic structures, J. G¨okova Geom. Topol. GGT 2 (2008), 40-82. · Zbl 1214.57027 |
| [2] | P. J. Callahan, J. C. Dean, and J. R. Weeks, The simplest hyperbolic knots, J. Knot Theory Ramifications 8 (1999), no. 3, 279-297. · Zbl 0933.57010 |
| [3] | J. C. Dean, Hyperbolic knots with small Seifert-fibered Dehn surgeries, Thesis (Ph.D.)The University of Texas at Austin, 1996. RATIONAL HOMOLOGY BALLS IN 2-HANDLEBODIES1933 |
| [4] | R. Fintushel and R. Stern, Rational blowdowns of smooth 4-manifolds, J. Differential Geom. 46 (1997), no. 2, 181-235. · Zbl 0896.57022 |
| [5] | R. Gompf and A. Stipsicz, 4-manifolds and Kirby calculus, Graduate Studies in Mathematics 20, American Mathematical Society, Providence, RI, 1999. · Zbl 0933.57020 |
| [6] | P. Hacking, J. Tevelev, and G. Urz´ua, Flipping surfaces, J. Algebraic Geom. 26 (2017), no. 2, 279-345. · Zbl 1360.14055 |
| [7] | T. Khodorovskiy, Smooth embeddings of rational homology balls, Topology Appl. 161 (2014), 386-396. · Zbl 1408.57030 |
| [8] | B. Owens, Equivariant embeddings of rational homology balls, arXiv:1707.00928. · Zbl 1405.57007 |
| [9] | H. Park, J. Park, and D. Shin. Smoothly embedded rational homology balls, J. Korean Math. Soc. 53 (2016), no. 6, 1293-1308. · Zbl 1361.57036 |
| [10] | J. Park, Seiberg-Witten invariants of generalised rational blow-downs, Bull. Austral. Math. Soc. 56 (1997), no. 3, 363-384. · Zbl 0892.57020 |
| [11] | , Simply connected symplectic 4-manifolds with b+2= 1 and c21= 2, Invent. Math. 159 (2005), no. 3, 657-667. · Zbl 1080.57030 |
| [12] | J. Park, A. Stipsicz, and Z. Szab´o. Exotic smooth structures on CP2#5CP2, Math. Res. Lett. 12 (2005), no. 5-6, 701-712. · Zbl 1081.57025 |
| [13] | A. Stipsicz and Z. Szab´o. An exotic smooth structure on CP2#6CP2, Geom. Topol. 9 (2005), 813-832. · Zbl 1077.57025 |
| [14] | F. Vafaee, On the knot Floer homology of twisted torus knots, Int. Math. Res. Not. IMRN 2015 (2015), no. 15, 6516-6537. · Zbl 1354.57018 |
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