Equivariant Rho-Invariants and Instanton Homology of Torus Knots

Nima Anvari

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arXiv · 1609.05025

Equivariant Rho-Invariants and Instanton Homology of Torus Knots

Nima Anvari

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Abstract

The equivariant rho-invariants studied in this paper are a version of the classical rho-invariants of Atiyah, Patodi, and Singer in the presence of an isometric involution. We compute these rho-invariants for all involutions on the 3-dimensional lens spaces with 1-dimensional fixed point sets, as well as for some involutions on Brieskorn homology spheres. As an application, we compute the generators and Floer gradings in the singular instanton chain complex of (p,q)-torus knots with odd p and q.

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Nima Anvari. 2016-09-16. Equivariant Rho-Invariants and Instanton Homology of Torus Knots. https://arxiv.org/abs/1609.05025

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