Twisted Blanchfield pairings and symmetric chain complexes

Powell, M. (2016) Twisted Blanchfield pairings and symmetric chain complexes. Quarterly Journal of Mathematics, 67(4), pp. 715-742. (doi: 10.1093/qmath/haw028)

Abstract

We define the twisted Blanchfield pairing of a symmetric triad of chain complexes over a group ring ℤ[π]⁠, together with a unitary representation of π over an Ore domain with involution. We prove that the pairing is sesquilinear, and we prove that it is hermitian and non-singular under certain extra conditions. A twisted Blanchfield pairing is then associated to a 3-manifold together with a decomposition of its boundary into two pieces, and a unitary representation of its fundamental group.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Powell, Dr Mark
• Authors: Powell, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Quarterly Journal of Mathematics
• Publisher: Oxford University Press
• ISSN: 0033-5606
• ISSN (Online): 1464-3847
• Published Online: 30 November 2016
• Copyright Holders: Copyright © 2016 Oxford University Press
• First Published: First published in Quarterly Journal of Mathematics 67(4): 715-742
• Publisher Policy: Reproduced in accordance with the publisher copyright policy