Homology spheres with E₈-fillings and arbitrarily large correction terms

2018/11/28 by Motoo Tange, Tange, Motoo
Computer Science · Mathematics · #57M27 #57R65 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GT #msc:57M27 #msc:57R65

paper · pdf · doi:10.48550/arxiv.1811.11831

14 pages, 2 figures. Comments are welcome

arxiv created 2018/11/28 · openalex publication_date 2018/11/28 · arxiv updated 2018/11/30 · openalex created_date 2018/12/11 · openalex updated_date 2026/07/28

Abstract

In this paper we construct families of homology spheres which bound 4-manifolds with intersection forms isomorphic to -E₈. We show that these families have arbitrary large correction terms. This result says that among homology spheres, the difference of the maximal rank of minimal sub-lattice of definite filling and the maximal rank of even definite filling is arbitrarily large.

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