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Cycles, submanifolds, and structures on normal bundles

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arxiv math/0011178 v2 pith:ORIYWUHX submitted 2000-11-22 math.GT hep-thmath.AT

C. Bohr , B. Hanke , D. Kotschick This is my paper · ORCID
classification math.GThep-thmath.AT
keywords submanifoldsbundlesclassesnormalcohomologycyclesdegreediscuss
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We give explicit examples of degree 3 cohomology classes not Poincare dual to submanifolds, and discuss the realisability of homology classes by submanifolds with Spin-C normal bundles.

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  1. On Realisability of Twisted Homology

    math.AT 2026-07 accept novelty 7.5 of 10

    A twisted homology class is realised by a submanifold iff its Poincaré dual is pulled back from the twisted Thom class of M^tw O(n) via a map over BO(1); the first non-realisable examples in non-orientable manifolds a...

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