Contents Introduction 1 Chapter 1. Maps from Loop Suspensions to Loop Spaces 9 1.1. The James Construction 9 1.2. Bi-A-groups 16 1.3. Skeletons of Bi-A-groups 26 1.4. The Cohen Construction 31 Chapter 2. Shuffle Relations 39 2.1. Functors to Coalgebras 39 2.2. Geometric Realizations and the Shuffle Relations 53 2.3. Proof of Theorem 3 56 2.4. Proof of Theorem 4 58 Bibliography 63
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