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 Rational homology balls in 2-handlebodies Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 1927-1933 https://doi.org/10.4134/BKMS.b160509Published online November 30, 2017 Heesang Park, Dongsoo Shin Konkuk University, Chungnam National University Abstract : 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. Keywords : $2$-handlebody, knot, rational blow-down, rational homology ball MSC numbers : 57R40, 57R55 Downloads: Full-text PDF