Concordance Invariants from Higher Order Covers
نویسنده
چکیده
We generalize the Manolescu-Owens smooth concordance invariant δ(K) of knots K ⊂ S to invariants δpn(K) obtained by considering covers of order p, with p a prime. Our main result shows that for any prime p 6= 2, the thus obtained homomorphism ⊕n∈Nδpn from the smooth concordance group to Z∞ has infinite rank. We also show that unlike δ, these new invariants typically are not multiples of the knot signature, even for alternating knots. A significant portion of the article is devoted to exploring examples.
منابع مشابه
Signature Invariants of Links from Irregular Covers and Non-abelian Covers
Abstract. Signature invariants of odd dimensional links from irregular covers and non-abelian covers of complements are obtained by using the technique of Casson and Gordon. We show that the invariants vanish for slice links and can be considered as invariants under Fm-link concordance. We illustrate examples of links that are not slice but behave as slice links for any invariants from abelian ...
متن کاملHigher-order Genera of Knots
For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higherorder genera in terms of certain von Neumann ρ-invariants, which we call higher-order signatures. The higher-order genera offer a refinement of the Grope filtration of the knot concordance group.
متن کاملLINK CONCORDANCE, HOMOLOGY COBORDISM, AND HIRZEBRUCH-TYPE DEFECTS FROM ITERATED p-COVERS
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary depth of the derived series of the fundamental group, and can detect torsion which is invisible via signature invariants. Applications illustrating these fe...
متن کاملLINK CONCORDANCE, HOMOLOGY COBORDISM, AND HIRZEBRUCH-TYPE INTERSECTION FORM DEFECTS FROM TOWERS OF ITERATED p-COVERS
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary depth of the derived series of the fundamental group, and can detect torsion which is invisible via signature invariants. Applications illustrating these fe...
متن کاملWhitney tower concordance of classical links
This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney...
متن کامل