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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.
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참고문헌 (14)
참고문헌 신청
A. Stipsicz / 2005 / An exotic smooth structure on CP2#6CP2 / Geom. Topol 9 : 813 ~ 832
B. Owens / / Equivariant embeddings of rational homology balls / arXiv:1707.00928
F. Vafaee / 2015 / On the knot Floer homology of twisted torus knots / Int. Math. Res. Not. IMRN 2015 (15) : 6516 ~ 6537
J. C. Dean / 1996 / Hyperbolic knots with small Seifert-fibered Dehn surgeries / Ph.D. / The University of Texas at Austin
J. Park / 1997 / Seiberg-Witten invariants of generalised rational blow-downs / Bull. Austral. Math. Soc 56 (3) : 363 ~ 384
B. Owens / / Equivariant embeddings of rational homology balls / arXiv:1707.00928
F. Vafaee / 2015 / On the knot Floer homology of twisted torus knots / Int. Math. Res. Not. IMRN 2015 (15) : 6516 ~ 6537
J. C. Dean / 1996 / Hyperbolic knots with small Seifert-fibered Dehn surgeries / Ph.D. / The University of Texas at Austin
J. Park / 1997 / Seiberg-Witten invariants of generalised rational blow-downs / Bull. Austral. Math. Soc 56 (3) : 363 ~ 384
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