2014/08/23 by Motoo Tange, Tange, Motoo · 1 citation
Chemistry · Mathematics · #57R55 #57R65 #Algebraic structures and combinatorial models #Artificial intelligence #Betti number #Bounding overwatch #Chemistry #Combinatorics #Computer science #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Physics #Product (mathematics) #Pure mathematics #SPHERES #math.GT #msc:57R55 #msc:57R65
paper · pdf · doi:10.48550/arxiv.1408.5528
published in arXiv (Cornell University) (Cornell University) · 24 pages, 16 figures
arxiv created 2014/08/23 · openalex publication_date 2014/08/23 · arxiv updated 2014/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We define invariants \frakds and \frakds, which are the maximal and minimal second Betti number divided by 8 among definite spin boundings of a homology sphere. The similar invariants g8 and g8 are defined by the maximal (or minimal) product sum of E8-form of bounding 4-manifolds. We compute these invariants for some homology spheres. We construct E8-boundings for some of Brieskorn 3-spheres Σ(2,3,12n+5) by handle decomposition. As a by-product of the construction, some negative classes which consist of addition of several fiber classes plus one sectional class in E(1) are represented by spheres.