Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(6): 1927-1933

Online first article November 8, 2017      Printed November 30, 2017

https://doi.org/10.4134/BKMS.b160509

Copyright © The Korean Mathematical Society.

Rational homology balls in 2-handlebodies

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