Abstract
In this article, using combinatorial techniques of mapping class groups, we show that a Stein fillable integral homology 3-sphere supported by an open book with page a 4-holed sphere admits a unique Stein filling up to symplectic deformation. Furthermore, according to a property of deforming symplectic fillings of rational homology 3-spheres into strong symplectic fillings, we also show that a symplectically fillable integral homology 3-sphere supported by an open book with page a 4-holed sphere admits a unique symplectic filling up to symplectic deformation and blow-up.
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Acknowledgments
The author would like to express his gratitude to Professor Hisaaki Endo for his encouragement and many helpful comments for the draft of this article. He would also like to thank Motoo Tanage, Kouichi Yasui and the anonymous referee for their useful and kindly comments on this article. In particular, he would also like to thank Chris Wendl for informing him of a forthcoming result of Lisi, Van Horn-Morris and Wendl.
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Oba, T. Stein fillings of homology 3-spheres and mapping class groups. Geom Dedicata 183, 69–80 (2016). https://doi.org/10.1007/s10711-016-0146-4
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DOI: https://doi.org/10.1007/s10711-016-0146-4