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In this paper, we introduce several new secondary invariants for Dirac operators on a complete Riemannian manifold with a uniform positive scalar curvature metric outside a compact set and use these secondary invariants to establish a higher index theorem for the Dirac operators. We apply our theory to study the secondary invariants for a manifold with corner with positive scalar curvature metric on each boundary face.
Higher index of signature operator is a far reaching generalization of signature of a closed oriented manifold. When two closed oriented manifolds are homotopy equivalent, one can define a secondary invariant of the relative signature operator called
In this paper, we adapt part of Weinberger, Xie and Yus breakthrough work, to define additive higher rho invariant for topological structure group by differential geometric version of signature operators, or in other words, unbounded Hilbert-Poincar{e} complexes.
In this paper, we define the relative higher $rho$ invariant for orientation preserving homotopy equivalence between PL manifolds with boundary in $K$-theory of the relative obstruction algebra, i.e. the relative analytic structure group. We also sho
The collinear factorization framework allows to describe the exclusive photoproduction of a $gamma,rho$ pair in the generalized Bjorken regime in terms of a perturbatively calculable coefficient function and universal generalized parton distributions
We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $sgeq 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case this formalism is equivalent to the theory of $mathsf{U}(1)$ duality-i