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3-manifolds that bound no definite 4-manifold

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 نشر من قبل Kyle Larson
 تاريخ النشر 2020
  مجال البحث
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We produce a rational homology 3-sphere that does not smoothly bound either a positive or negative definite 4-manifold. Such a 3-manifold necessarily cannot be rational homology cobordant to a Seifert fibered space or any 3-manifold obtained by Dehn surgery on a knot. The proof requires an analysis of short characteristic covectors in bimodular lattices.



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