On maps from loop suspensions to loop spaces and the shuffle relations on the Cohen groups / Jie Wu.

Format:

Book

Author/Creator:

Wu, Jie, 1964- author.

Series:

Memoirs of the American Mathematical Society ; no. 851.

Memoirs of the American Mathematical Society, 0065-9266 ; number 851

Language:

English

Subjects (All):

Homotopy theory.

Algebra, Homological.

Representations of groups.

Algebraic topology.

Physical Description:

1 online resource (78 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2006]

Language Note:

English

Summary:

The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy theory are displayed in the extension groups of the dual of the important symmetric group modules Lie$(n)$, as well as in the top cohomology of the Artin braid groups with coefficients in the top homology of the Artin pure braid groups.

Contents:

""Contents""; ""Introduction""; ""Chapter 1. Maps from Loop Suspensions to Loop Spaces""; ""1.1. The James Construction""; ""1.2. Bi-Î?-groups""; ""1.3. Skeletons of Bi-Î?-groups""; ""1.4. The Cohen Construction""; ""Chapter 2. Shuffle Relations""; ""2.1. Functors to Coalgebras""; ""2.2. Geometric Realizations and the Shuffle Relations""; ""2.3. Proof of Theorem 3""; ""2.4. Proof of Theorem 4""; ""Bibliography""

Notes:

"Volume 180, number 851 (end of volume)."

Includes bibliographical references (pages 63-64).

Description based on print version record.

ISBN:

1-4704-0455-9