Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
On Finite Groups and Homotopy Theory
 
Ran Levi University of Heidelberg
Front Cover for On Finite Groups and Homotopy Theory
Available Formats:
Electronic ISBN: 978-1-4704-0146-7
Product Code: MEMO/118/567.E
List Price: $44.00
MAA Member Price: $39.60
AMS Member Price: $26.40
Front Cover for On Finite Groups and Homotopy Theory
Click above image for expanded view
  • Front Cover for On Finite Groups and Homotopy Theory
  • Back Cover for On Finite Groups and Homotopy Theory
On Finite Groups and Homotopy Theory
Ran Levi University of Heidelberg
Available Formats:
Electronic ISBN:  978-1-4704-0146-7
Product Code:  MEMO/118/567.E
List Price: $44.00
MAA Member Price: $39.60
AMS Member Price: $26.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1181996; 100 pp
    MSC: 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 non-trivial \(k\)-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.

    Readership

    Researchers 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. Clark-Ewing spaces and groups
    • 7. Discussion
  • Request Review Copy
  • Get Permissions
Volume: 1181996; 100 pp
MSC: 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 non-trivial \(k\)-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.

Readership

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. Clark-Ewing spaces and groups
  • 7. Discussion
Please select which format for which you are requesting permissions.