Geodesic
Double L–groups and doubly slice knots
Orson, Patrick1
1Department of Mathematics, Durham University, Lower Mountjoy, Stockton Road, Durham, DH1 3LE, United Kingdom
Algebraic and Geometric Topology, Tome 17 (2017) no. 1, pp. 273-329
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We develop a theory of chain complex double cobordism for chain complexes equipped with Poincaré duality. The resulting double cobordism groups are a refinement of the classical torsion algebraic L–groups for localisations of a ring with involution. The refinement is analogous to the difference between metabolic and hyperbolic linking forms.

We apply the double L–groups in high-dimensional knot theory to define an invariant for doubly slice n–knots. We prove that the “stably doubly slice implies doubly slice” property holds (algebraically) for Blanchfield forms, Seifert forms and for the Blanchfield complexes of n–knots for n ≥ 1.

DOI : 10.2140/agt.2017.17.273
Classification : 57Q45, 57R67, 57Q60, 57R65
Keywords: knot theory, L-theory, doubly slice, high-dimensional knot, Blanchfield pairing

Orson, Patrick  1

1 Department of Mathematics, Durham University, Lower Mountjoy, Stockton Road, Durham, DH1 3LE, United Kingdom 
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Orson, Patrick. Double L–groups and doubly slice knots. Algebraic and Geometric Topology, Tome 17 (2017) no. 1, pp. 273-329. doi: 10.2140/agt.2017.17.273

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