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In this paper we construct families of homology spheres which bound4-manifolds with intersection forms isomorphic to $-E_8$. We show that thesefamilies have arbitrary large correction terms. This result says that amonghomology spheres, the difference of the maximal rank of minimal sub-lattice ofdefinite filling and the maximal rank of even definite filling is arbitrarilylarge.

Homology spheres with $E_8$-fillings and arbitrarily large correction terms