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We apply the method of linear perturbations to the case of Spin(7)-structures, showing that the only nontrivial perturbations are those determined by a rank one nilpotent matrix. We consider linear perturbations of the Bryant-Salamon metric on the spin bundle over $S^4$ that retain invariance under the action of Sp(2), showing that the metrics obtained in this way are isometric.
The total space of the spinor bundle on the four dimensional sphere S^4 is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang-Mills instanton on this eight dimensional gravitational instanton. This is a h
We show for a certain class of operators $A$ and holomorphic functions $f$ that the functional calculus $Amapsto f(A)$ is holomorphic. Using this result we are able to prove that fractional Laplacians $(1+Delta^g)^p$ depend real analytically on the m
We formulate and study the isometric flow of $mathrm{Spin}(7)$-structures on compact $8$-manifolds, as an instance of the harmonic flow of geometric structures. Starting from a general perspective, we establish Shi-type estimates and a correspondence
In this paper we study ${rm Spin}(7)$-instantons on asymptotically conical ${rm Spin}(7)$-orbifolds (and manifolds) obtained by filling in certain squashed $3$-Sasakian $7$-manifolds. We construct a $1$-parameter family of explicit ${rm Spin}(7)$-ins
This paper generalizes Bismuts equivariant Chern character to the setting of abelian gerbes. In particular, associated to an abelian gerbe with connection, an equivariantly closed differential form is constructed on the space of maps of a torus into