The fundamental theorem via derived Morita invariance, localization, and 1-homotopy invariance

Obstructions to Homotopy Invariance

Homotopy invariance of higher signatures

We prove that the higher signature for any close oriented manifold is a homotopy invariant. 2000 MR Subject Classification 57N70, 57R95, 57R40

On the homotopy invariance of string topology

Let M be a closed, oriented, n-manifold, and LM its free loop space. In [C-S1] a commutative algebra structure in homology, H∗(LM), and a Lie algebra structure in equivariant homology H 1 ∗ (LM), were defined. In this paper we prove that these structures are homotopy invariant for simply connected manifolds in the following sense. Let f : M1 → M2 be a homotopy equivalence of simply connected cl...

A Simple Invariance Theorem

J. W. Lindeberg’s elegant proof of the Central Limit Theorem [15, 16], despite being in the shadow of Fourier analytic methods for a long time, is now well known. It was revived by Trotter [25] and has since been used successfully to derive CLTs in infinite dimensional spaces, where the Fourier analytic methods are not so useful. For more information on this topic, see the survey paper [3] and ...

Pull-backs of Bundles and Homotopy Invariance

We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article is to show that for a principal fibre bundle over paracompact manifolds, there is a principal fibre bundle isomorphism between pull-backs obtained from homoto...