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There is an explicit, but complicated, formula for going from the sectional curvature back to the curvature tensor in equation (1.10) on page 16 of Cheeger and Ebin's book.

I'm not familiar with that reference but a standard example for this is by Stephanie Halbeisen "On tangent cones of Alexandrov spaces with curvature bounded below". The example is necessarily infinite …

Let me call your $\omega$ as $\omega_I$. The symplectic form you get from the Chern-Simons action is $k\omega_I+s\omega_K$, where $\omega_K$ is one of the Kähler forms on the Hitchin space, which, in …

Look at Kist and Leestma - Additive semigroups of positive real numbers. It would seem in some sense to answer the question.

Nobody can even catalog the set of all subsets of positive integers closed under addition (aka subsemigroups of the infinite cyclic semigroup). See Repnitskii, Vladimir - On subsemigroup lattices wit …

Karl Auinger and I came up with the following proof which proves residually p and even stronger properties (e.g., residually finite of square-free exponent). Let me first introduce the main construct …

You do not need $\sigma$-finiteness of the measure in Fubini theorem, although it is an hypothesis that can be assumed with no loss of generality, in that the support of an integrable function is, of …

Are you also looking for holomorphic manifolds with $\dim \mathcal O=\infty$? In that case, in the paper by Sasane On the Krull Dimension of Rings of Transfer Functions [Acta Applicandae Mathematicae …

A favorite of mine is the chirality of the trefoil knot, which can be proved easily using the Jones polynomial or some of its relatives. Louis Kauffman's paper "New invariants in the theory of knots", …

Kurosh's original proof of the subgroup theorem for free products used messy Kurosh systems. This was improved by covering space proofs (or equivalently covering groupoid proofs). One might argue the …

There are several examples from Tauberian theory. Around 1930, Karamata surprised people by giving much simpler proofs of Littlewood's original Tauberian theorems for power series. Wiener's Tauberia …

See Warren P. Johnson, Combinatorics of Higher Derivatives of Inverses, American Mathematical Monthly, Vol. 109, No. 3 (Mar., 2002), pp. 273-277, http://www.jstor.org/stable/2695356

This is sometime called the Lagrange inversion formula.

Riordan's Combinatorial identities has a chapter on partition polynomials that may be helpful. It specifically covers the question you are asking, but is in umbral calculus.

Well well well, it seems like Witten has played a pretty nasty joke on all of us... And all the authors who copied from him apparently fell for it as well! But I found a possible resolution to the pr …