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Subgroup Complexes
 
Stephen D. Smith University of Illinois at Chicago, Chicago, IL
Subgroup Complexes
Hardcover ISBN:  978-0-8218-0501-5
Product Code:  SURV/179
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1406-1
Product Code:  SURV/179.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-0501-5
eBook: ISBN:  978-1-4704-1406-1
Product Code:  SURV/179.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Subgroup Complexes
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Subgroup Complexes
Stephen D. Smith University of Illinois at Chicago, Chicago, IL
Hardcover ISBN:  978-0-8218-0501-5
Product Code:  SURV/179
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1406-1
Product Code:  SURV/179.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-0501-5
eBook ISBN:  978-1-4704-1406-1
Product Code:  SURV/179.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1792011; 364 pp
    MSC: Primary 20; 05; 55;

    This book is intended as an overview of a research area that combines geometries for groups (such as Tits buildings and generalizations), topological aspects of simplicial complexes from \(p\)-subgroups of a group (in the spirit of Brown, Quillen, and Webb), and combinatorics of partially ordered sets. The material is intended to serve as an advanced graduate-level text and partly as a general reference on the research area. The treatment offers optional tracks for the reader interested in buildings, geometries for sporadic simple groups, and \(G\)-equivariant equivalences and homology for subgroup complexes.

    Readership

    Graduate students and research mathematicians interested in group theory and algebraic topology.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Part 1. Background material and examples
    • 1. Background: Posets, simplicial complexes, and topology
    • 2. Examples: Subgroup complexes as geometries for simple groups
    • Part 2. Fundamental techniques
    • 3. Contractibility
    • 4. Homotopy equivalence
    • Basic applications
    • 5. The reduced Euler characteristic ${\tilde {\chi }}$ and variations on vanishing
    • 6. The reduced Lefschetz module ${\tilde {L}}$ and projectivity
    • 7. Group cohomology and decompositions
    • Part 3. Some more advanced topics
    • 8. Spheres in homology and Quillen’s Conjecture
    • 9. Connectivity, simple connectivity, and sphericality
    • 10. Local-coefficient homology and representation theory
    • 11. Orbit complexes and Alperin’s Conjecture
  • Reviews
     
     
    • There is an informal and conversational style to the description, designed to lead the reader through the story. This is extremely valuable for motivation and accessibility...

      Mathematical Reviews
  • 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
Volume: 1792011; 364 pp
MSC: Primary 20; 05; 55;

This book is intended as an overview of a research area that combines geometries for groups (such as Tits buildings and generalizations), topological aspects of simplicial complexes from \(p\)-subgroups of a group (in the spirit of Brown, Quillen, and Webb), and combinatorics of partially ordered sets. The material is intended to serve as an advanced graduate-level text and partly as a general reference on the research area. The treatment offers optional tracks for the reader interested in buildings, geometries for sporadic simple groups, and \(G\)-equivariant equivalences and homology for subgroup complexes.

Readership

Graduate students and research mathematicians interested in group theory and algebraic topology.

  • Chapters
  • Introduction
  • Part 1. Background material and examples
  • 1. Background: Posets, simplicial complexes, and topology
  • 2. Examples: Subgroup complexes as geometries for simple groups
  • Part 2. Fundamental techniques
  • 3. Contractibility
  • 4. Homotopy equivalence
  • Basic applications
  • 5. The reduced Euler characteristic ${\tilde {\chi }}$ and variations on vanishing
  • 6. The reduced Lefschetz module ${\tilde {L}}$ and projectivity
  • 7. Group cohomology and decompositions
  • Part 3. Some more advanced topics
  • 8. Spheres in homology and Quillen’s Conjecture
  • 9. Connectivity, simple connectivity, and sphericality
  • 10. Local-coefficient homology and representation theory
  • 11. Orbit complexes and Alperin’s Conjecture
  • There is an informal and conversational style to the description, designed to lead the reader through the story. This is extremely valuable for motivation and accessibility...

    Mathematical Reviews
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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