eBook ISBN:  9781470401467 
Product Code:  MEMO/118/567.E 
List Price:  $44.00 
MAA Member Price:  $39.60 
AMS Member Price:  $26.40 
eBook ISBN:  9781470401467 
Product Code:  MEMO/118/567.E 
List Price:  $44.00 
MAA Member Price:  $39.60 
AMS Member Price:  $26.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 118; 1996; 100 ppMSC: Primary 55
Let \(p\) be a fixed prime number. Let \(G\) denote a finite \(p\)perfect group. This book looks at the homotopy type of the \(p\)completed classifying space \(BG_p\), where \(G\) is a finite \(p\)perfect group. The author constructs an algebraic analog of the Quillen's “plus” construction for differential graded coalgebras. This construction is used to show that given a finite \(p\)perfect group \(G\), the loop spaces \(BG_p\) admits integral homology exponents. Levi gives examples to show that in some cases our bound is best possible. It is shown that in general \(B\ast _p\) admits infinitely many nontrivial \(k\)invariants. The author presents examples where homotopy exponents exist. Classical constructions in stable homotopy theory are used to show that the stable homotopy groups of these loop spaces also have exponents.
ReadershipResearchers in algebraic topology, and finite group theory and homotopy theory.

Table of Contents

Chapters

Part 1. The homology and homotopy theory associated with $\Omega B\pi _p^\wedge $

1. Introduction

2. Preliminaries

3. A model for $S_*{\Omega }X^\wedge _R$

4. Homology exponents for ${\Omega }B\pi ^\wedge _p$

5. Examples for homology exponents

6. The homotopy groups of $B\pi ^\wedge _p$

7. Stable homotopy exponents for ${\Omega }B\pi ^\wedge _p$

Part 2. Finite groups and resolutions by fibrations

1. Introduction

2. Preliminaries

3. Resolutions by fibrations

4. Sporadic examples

5. Groups of Lie type and $\mathcal {S}$resolutions

6. ClarkEwing spaces and groups

7. Discussion


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Let \(p\) be a fixed prime number. Let \(G\) denote a finite \(p\)perfect group. This book looks at the homotopy type of the \(p\)completed classifying space \(BG_p\), where \(G\) is a finite \(p\)perfect group. The author constructs an algebraic analog of the Quillen's “plus” construction for differential graded coalgebras. This construction is used to show that given a finite \(p\)perfect group \(G\), the loop spaces \(BG_p\) admits integral homology exponents. Levi gives examples to show that in some cases our bound is best possible. It is shown that in general \(B\ast _p\) admits infinitely many nontrivial \(k\)invariants. The author presents examples where homotopy exponents exist. Classical constructions in stable homotopy theory are used to show that the stable homotopy groups of these loop spaces also have exponents.
Researchers in algebraic topology, and finite group theory and homotopy theory.

Chapters

Part 1. The homology and homotopy theory associated with $\Omega B\pi _p^\wedge $

1. Introduction

2. Preliminaries

3. A model for $S_*{\Omega }X^\wedge _R$

4. Homology exponents for ${\Omega }B\pi ^\wedge _p$

5. Examples for homology exponents

6. The homotopy groups of $B\pi ^\wedge _p$

7. Stable homotopy exponents for ${\Omega }B\pi ^\wedge _p$

Part 2. Finite groups and resolutions by fibrations

1. Introduction

2. Preliminaries

3. Resolutions by fibrations

4. Sporadic examples

5. Groups of Lie type and $\mathcal {S}$resolutions

6. ClarkEwing spaces and groups

7. Discussion