Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Loop Space Splittings of Sphere Bundles over Highly Connected Poincaré Complexes

Wen Shen

Abstract

Let $m > n \ge 2$, and let $N$ be an $(n-1)$-connected $2n$-Poincaré complex. In this paper, we establish sufficient conditions under which the loop space of the total space $M$ of the sphere bundle $S^{m-1} \to M \to N$ (associated to a rank-$m$ real vector bundle over $N$) splits as a product of the loop spaces of $N$ and $S^{m-1}$.

Loop Space Splittings of Sphere Bundles over Highly Connected Poincaré Complexes

Abstract

Let , and let be an -connected -Poincaré complex. In this paper, we establish sufficient conditions under which the loop space of the total space of the sphere bundle (associated to a rank- real vector bundle over ) splits as a product of the loop spaces of and .

Paper Structure

This paper contains 3 sections, 32 equations.

Table of Contents

  1. Introduction
  2. Vector bundles over highly connected complexes
  3. Proof of Theorem \ref{['mainth']}

Theorems & Definitions (7)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof : Proof of Item (1) of Theorem \ref{['mainth']}
  • proof : Proof of Item (3) of Theorem