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
–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
–groups
in high-dimensional knot theory to define an invariant for doubly slice
–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
–knots
for
.
We have not been able to recognize your IP address
54.236.58.220
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.