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On Finite Groups and Homotopy Theory
 
Ran Levi :  University of Heidelberg
On Finite Groups and Homotopy Theory
eBook 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
Add to cart
On Finite Groups and Homotopy Theory
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On Finite Groups and Homotopy Theory
Ran Levi :  University of Heidelberg
eBook 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
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 118; 1996; 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 118; 1996; 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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