Pure and Applied Mathematics Quarterly

Volume 13 (2017)

Number 3

Special Issue in Honor of Simon Donaldson

Guest Editors: Kefeng Liu, Richard Thomas, and Shing-Tung Yau

Orientability of the moduli space of $\mathrm{Spin}(7)$-instantons

Pages: 453 – 476

DOI: https://dx.doi.org/10.4310/PAMQ.2017.v13.n3.a4

Authors

Vicente Muñoz (Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Spain)

C. S. Shahbazi (Institut für Theoretische Physik, Leibniz Universität Hannover, Germany)

Abstract

Let $(M, \Omega)$ be a closed $8$-dimensional manifold equipped with a generically non-integrable $\mathrm{Spin}(7)$-structure $\Omega$. We prove that if $\mathrm{Hom}(H^3 (M, \mathbb{Z}), \mathbb{Z}_2) = 0$ then the moduli space of irreducible $\mathrm{Spin}(7)$-instantons on $(M, \Omega)$ with gauge group $SU(r), r \geq 2$, is orientable.

Keywords

$\mathrm{Spin}(7)$-instanton, moduli space, $\mathrm{Spin}(7)$-structure

2010 Mathematics Subject Classification

Primary 53C38. Secondary 53C07, 53C25.

Full Text (PDF format)

In commemoration of the 60th birthday of Prof. Simon Donaldson, with our utmost gratitude for all we have learnt from him.

The first author was partially supported through Project MICINN (Spain) MTM2015-63612-P.

Second author was partially supported by the German Science Foundation (DFG) Project LE838/13.

Received 8 July 2017

Published 12 November 2018