This is a monograph that details the use of Siegel s method and the classical results of homotopy groups of spheres and Lie groups to determine some Gottlieb groups of projective spaces or to give the lower bounds of their orders. Making use of the properties of Whitehead products, the authors also determine some Whitehead center groups of projective spaces that are relevant and new within this monograph.
Introduction.- Gottlieb groups of Spheres.- Gottlieb and Whitehead Center Groups of Projective Spaces.- Gottlieb and Whitehead Center Groups of Moore Spaces.
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1 Gottlieb Groups of Spheres |
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1 | (48) |
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1.1 Preliminaries on Gottlieb Groups |
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1 | (9) |
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1.2 Gottlieb Groups of Spheres with Stems for κ ≤ 7 |
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10 | (6) |
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1.3 Proof of Theorem 1.14, Part I |
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16 | (8) |
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1.4 Proof of Theorem 1.14, Part II |
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24 | (11) |
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1.5 Proof of [ ι16s+7, σ16.v+7] ≠ 0 for s ≥ 1 |
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35 | (3) |
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1.6 Gottlieb Groups of Spheres with Stems for 8 ≤ κ ≤ 13 |
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38 | (11) |
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2 Gottlieb and Whitehead Center Groups of Projective Spaces |
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49 | (56) |
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49 | (7) |
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56 | (5) |
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2.3 Whitehead Center Groups of Projective Spaces |
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61 | (3) |
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2.4 Some Whitehead Center Groups of Real Projective Spaces |
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64 | (9) |
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2.5 Some Whitehead Center Groups of Complex and Quaternionic Projective Spaces |
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73 | (8) |
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2.6 Gottlieb Groups of Real Projective Spaces |
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81 | (8) |
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2.7 Gottlieb Groups of Complex and Quaternionic Projective Spaces |
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89 | (9) |
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2.8 The Case of the Cayley Projective Plane |
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98 | (7) |
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3 Gottlieb and Whitehead Center Groups of Moore Spaces |
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105 | (22) |
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3.1 Gottlieb and Whitehead Center Groups of Mod 2 Moore Spaces |
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105 | (5) |
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3.2 Gottlieb Groups of Some Moore Spaces M(A, n) |
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110 | (17) |
| References |
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127 | (4) |
| Index |
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131 | |
(1) Marek Golasinski Institute of Mathematics Casimir the Great University pl. Weyssenhoffa 11 85-07 2 Bydgoszcz, Poland e-mail: marek@ukw.edu.pl (2) Juno Mukai Shinshu University Matsumoto, Nagano Pref. 390-8621, Japan e-mail: jmukai@shinshu-u.ac.jp
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