We consider generators of algebraic covariant derivative curvature tensors R which can be constructed by a Young symmetrization of product tensors W ⊗ U or U ⊗ W , where W and U are covariant tensors of order 2 and 3. W is a symmetric or alternating tensor whereas U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2 1). Using Computer Alge...

We derive an index theorem for the Dirac operator in the background of various topological excitations on an R × S geometry. The index theorem provides more refined data than the APS index for an instanton on R and reproduces it in decompactification limit. In the R limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the η-invariant associat...

We derive an index theorem for the Dirac operator in the background of various topological excitations on an R × S geometry. The index theorem provides more refined data than the APS index for an instanton on R and reproduces it in decompactification limit. In the R limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the η-invariant associat...

We attempt a broad exploration of properties and connections between the symmetry function of a convex set S ⊂ IRn and other arenas of convexity including convex functions, convex geometry, probability theory on convex sets, and computational complexity. Given a point x ∈ S, let sym(x, S) denote the symmetry value of x in S: sym(x, S) := max{α ≥ 0 : x + α(x− y) ∈ S for every y ∈ S} , which esse...