On Finite Groups and Homotopy Theory.
Levi, Ran.
On Finite Groups and Homotopy Theory. - 1st ed. - 1 online resource (121 pages) - Memoirs of the American Mathematical Society ; v.118 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Abstract -- Preface -- Acknowledgements -- Part 1: The Homology and Homotopy Theory Associated with ΩBπ[sup(^)[sub(p)] -- Chapter 1. Introduction -- 1.1. Statement of Results -- 1.2. Organization of Part 1 -- Chapter 2. Preliminaries -- 2.1. Some Facts on the R-Completion Functor -- 2.2. Mod-R Acyclic Spaces and Proposition 1.1.2 -- 2.3. The Quillen "Plus" Construction -- Chapter 3. A model for S[sub(*)]ΩX[sup(^)sub(R)] -- 3.1. An Algebraic "Plus" Construction -- 3.2. Proof of Theorems 1.1.2 and 1.1.3 -- Chapter 4. Homology Exponents for ΩBπ[sup(^)[sub(p)] -- 4.1. Extended Maps and Homotopies -- 4.2. Proof of Theorem 1.1.1 -- Chapter 5. Examples for Homology Exponents -- 5.1. Groups with a Dihedral Sylow 2-Subgroup -- 5.2. Groups with a Semidihedral Sylow 2-Subgroup -- Chapter 6. The Homotopy Groups of Bπ[sup(^)[sub(p)] -- 6.1. Some Basic Facts -- 6.2. Proof of Theorem 1.1.4 -- 6.3. Examples for Homotopy Exponents -- Chapter 7. Stable Homotopy Exponents for ΩBπ[sup(^)[sub(p)] -- 7.1. Preliminaries on the Transfer -- 7.2. Proof of Theorem 1.1.5 -- 7.3. The Non Existence of Exponents in π[sup(s)[sub(*)]ΩBπ[sup(^)[sub(p)] -- Part 2: Finite Groups and Resolutions by Fibrations -- Chapter 1. Introduction -- 1.1. Statement of Results -- 1.2. Organization of Part 2 -- Chapter 2. Preliminaries -- 2.1. Universal Central Extensions -- 2.2. Uniqueness of Homotopy Type, Special Case -- 2.3. Homotopy decomposition of Classifying Spaces -- 2.4. The Neisendorfer Fibre Square Lemma -- Chapter 3. Resolutions by Fibrations -- 3.1. Definition and Basic Examples -- 3.2. A Fibration Lemma -- 3.3. The mod-p Cohen Conjecture -- Chapter 4. Sporadic Examples -- 4.1. Groups with a Dihedral Sylow 2-Subgroup -- 4.2. Groups with a Semidihedral Sylow 2-Subgroup -- Chapter 5. Groups of Lie Type and S-Resolutions -- 5.1. Preliminary Theorems. 5.2. A Spherical Fibre Square -- 5.3. Proof of Theorem 1.1.3 -- 5.4. The Groups SL[sub(n)](F[sub(q)] and Sp[sub(2n)](F[sub(q)] -- 5.5. Proof of Theorem 1.1.6 and Examples -- Chapter 6. Clark-Ewing Spaces and Groups -- 6.1. Construction -- 6.2. Spherical Resolutions of Loop Spaces on Clark-Ewing Spaces -- 6.3. Resolutions by Cohomological Considerations -- 6.4. Some Preliminaries from Representation Theory -- 6.5. Clark-Ewing Groups -- Chapter 7. Discussion -- References.
9781470401467
Finite groups.
Homotopy theory.
Loop spaces.
Electronic books.
QA177 -- .L485 1995eb
514/.24
On Finite Groups and Homotopy Theory. - 1st ed. - 1 online resource (121 pages) - Memoirs of the American Mathematical Society ; v.118 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Abstract -- Preface -- Acknowledgements -- Part 1: The Homology and Homotopy Theory Associated with ΩBπ[sup(^)[sub(p)] -- Chapter 1. Introduction -- 1.1. Statement of Results -- 1.2. Organization of Part 1 -- Chapter 2. Preliminaries -- 2.1. Some Facts on the R-Completion Functor -- 2.2. Mod-R Acyclic Spaces and Proposition 1.1.2 -- 2.3. The Quillen "Plus" Construction -- Chapter 3. A model for S[sub(*)]ΩX[sup(^)sub(R)] -- 3.1. An Algebraic "Plus" Construction -- 3.2. Proof of Theorems 1.1.2 and 1.1.3 -- Chapter 4. Homology Exponents for ΩBπ[sup(^)[sub(p)] -- 4.1. Extended Maps and Homotopies -- 4.2. Proof of Theorem 1.1.1 -- Chapter 5. Examples for Homology Exponents -- 5.1. Groups with a Dihedral Sylow 2-Subgroup -- 5.2. Groups with a Semidihedral Sylow 2-Subgroup -- Chapter 6. The Homotopy Groups of Bπ[sup(^)[sub(p)] -- 6.1. Some Basic Facts -- 6.2. Proof of Theorem 1.1.4 -- 6.3. Examples for Homotopy Exponents -- Chapter 7. Stable Homotopy Exponents for ΩBπ[sup(^)[sub(p)] -- 7.1. Preliminaries on the Transfer -- 7.2. Proof of Theorem 1.1.5 -- 7.3. The Non Existence of Exponents in π[sup(s)[sub(*)]ΩBπ[sup(^)[sub(p)] -- Part 2: Finite Groups and Resolutions by Fibrations -- Chapter 1. Introduction -- 1.1. Statement of Results -- 1.2. Organization of Part 2 -- Chapter 2. Preliminaries -- 2.1. Universal Central Extensions -- 2.2. Uniqueness of Homotopy Type, Special Case -- 2.3. Homotopy decomposition of Classifying Spaces -- 2.4. The Neisendorfer Fibre Square Lemma -- Chapter 3. Resolutions by Fibrations -- 3.1. Definition and Basic Examples -- 3.2. A Fibration Lemma -- 3.3. The mod-p Cohen Conjecture -- Chapter 4. Sporadic Examples -- 4.1. Groups with a Dihedral Sylow 2-Subgroup -- 4.2. Groups with a Semidihedral Sylow 2-Subgroup -- Chapter 5. Groups of Lie Type and S-Resolutions -- 5.1. Preliminary Theorems. 5.2. A Spherical Fibre Square -- 5.3. Proof of Theorem 1.1.3 -- 5.4. The Groups SL[sub(n)](F[sub(q)] and Sp[sub(2n)](F[sub(q)] -- 5.5. Proof of Theorem 1.1.6 and Examples -- Chapter 6. Clark-Ewing Spaces and Groups -- 6.1. Construction -- 6.2. Spherical Resolutions of Loop Spaces on Clark-Ewing Spaces -- 6.3. Resolutions by Cohomological Considerations -- 6.4. Some Preliminaries from Representation Theory -- 6.5. Clark-Ewing Groups -- Chapter 7. Discussion -- References.
9781470401467
Finite groups.
Homotopy theory.
Loop spaces.
Electronic books.
QA177 -- .L485 1995eb
514/.24