Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers - Mathematics > Geometric TopologyReportar como inadecuado




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Abstract: We obtain new invariants of topological link concordance and homologycobordism of 3-manifolds from Hirzebruch-type intersection form defects oftowers of iterated p-covers. Our invariants can extract geometric informationfrom an arbitrary depth of the derived series of the fundamental group, and candetect torsion which is invisible via signature invariants. Applicationsillustrating these features include the following: (1) There are infinitelymany homology equivalent rational 3-spheres which are indistinguishable viamultisignatures, eta-invariants, and L2-signatures but have distinct homologycobordism types. (2) There is an infinite family of 2-torsion (amphichiral)knots, including the figure eight knot, with non-slice iterated Bing doubles;as a special case, we give the first proof of the conjecture that the Bingdouble of the figure eight knot is not slice. (3) There exist infinitely manytorsion elements at any depth of the Cochran-Orr-Teichner filtration of linkconcordance.



Autor: Jae Choon Cha

Fuente: https://arxiv.org/







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