We prove that a general miraculous cancellation formula, the divisibility of certain characteristic numbers, and some other topological results related to the generalized Rochlin invariant, theâ€¦ (More)

Abstract. We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevichâ€™s stable map moduli spaces can be computed in termsâ€¦ (More)

where Ïˆi = c1(Li) is the first Chern class of Li, and Î»j = cj(E) is the j-th Chern class of the Hodge bundle. Hodge integrals arise in the calculations of Gromov-Witten invariants by localizationâ€¦ (More)

In this paper, we continue our study of the canonical metrics on the moduli space of curves. We first prove the bounded geometry of the Ricci and perturbed Ricci metrics. By carefully choosing theâ€¦ (More)

The main purpose of this paper is to give a simple and unified new proof of the Witten rigidity theorems, which were conjectured by Witten and first proved by Taubes [T], Bott-Taubes [BT], Hirzebruchâ€¦ (More)

In this paper we describe a proof of the formulas of Witten [W1], [W2] about the symplectic volumes and the intersection numbers of the moduli spaces of principal bundles on a compact Riemannâ€¦ (More)

We generalize the theorems in Mirror Principle I and II to the case of general projective manifolds without the convexity assumption. We also apply the results to balloon manifolds, and generalize toâ€¦ (More)

In this work we exploit the relationship with certain equivariant genera of isntanton moduli spaces to study the string partition functions of some local Calabi-Yau geometries, in particular, theâ€¦ (More)