Bordism, rho-invariants and the Baum–Connes conjecture

Bordism, rho-invariants and the Baum–Connes conjecture

Let ! be a finitely generated discrete group. In this paper we establish vanishing results for rho-invariants associated to (i) the spin Dirac operator of a spin manifold with positive scalar curvature and fundamental group !; (ii) the signature operator of the disjoint union of a pair of homotopy equivalent oriented manifolds with fundamental group ! . The invariants we consider are more preci...

Groups with torsion, bordism and rho-invariants

Let Γ be a discrete group, and let M be a closed spin manifold of dimension m > 3 with π1(M) = Γ. We assume that M admits a Riemannian metric of positive scalar curvature. We discuss how to use the L-rho invariant ρ(2) and the delocalized eta invariant η associated to the Dirac operator on M in order to get information about the space of metrics with positive scalar curvature. In particular ...

Elliptic Gromov-Witten Invariants And Virasoro Conjecture

The Virasoro conjecture predicts that the generating function of Gromov-Witten invariants is annihilated by infinitely many differential operators which form a half branch of the Virasoro algebra. This conjecture was proposed by Eguchi, Hori and Xiong [EHX2] and also by S. Katz [Ka] (see also [EJX]). It provides a powerful tool in the computation of Gromov-Witten invariants. In [LT], the author...

Elliptic Gromov-Witten invariants and the generalized mirror conjecture

A conjecture expressing genus 1 Gromov-Witten invariants in mirror-theoretic terms of semi-simple Frobenius structures and complex oscillating integrals is formulated. The proof of the conjecture is given for torus-equivariant Gromov Witten invariants of compact Kähler manifolds with isolated fixed points and for concave bundle spaces over such manifolds. Several results on genus 0 Gromov Witte...

The Su-bordism Theory