Polynomials and the mod 2 Steenrod algebra: Volume 1 The Peterson hit problem
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2018
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| Schriftenreihe: | London Mathematical Society lecture note series
441 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxiv, 346 Seiten |
| ISBN: | 9781108414487 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Titel: Bd. 1. Polynomials and the mod 2 Steenrod algebra. The Peterson hit problem
Autor: Walker, Grant
Jahr: 2018
London Mathematical Society Lecture Note Series: 441 Polynomials and the mod 2 Steenrod Algebra Volume 1: The Peterson Hit Problem GRANT {WALKER University of Manchester REGINALD M. W. WOOD University of Manchester 11 CAMBRIDGE UNIVERSITY PRESS
Contents of Volume 1 Contents of Volume 2 page xi Preface xv Steenrod squares and the hit problem 1 1.0 Introduction 1 1.1 The total square Sq 2 1.2 The action of matrices on P(/i) 4 1.3 Some properties of Scf 7 1.4 The hit problem 8 1.5 Spikes 12 1.6 The Kameko maps for P(2) 12 1.7 The duplication map for P(2) 14 1.8 The hit problem for P(2) 15 1.9 Remarks 17 Conjugate Steenrod squares 19 2.0 Introduction 19 2.1 Power series 19 2.2 The total conjugate square Xq 22 2.3 Some properties of Xcf 23 2.4 The numerical function p 26 2.5 The x-trick and the Peterson conjecture 28 2.6 Catalan numbers and Xqf 30 2.7 Remarks 31 The Steenrod algebra A2 33 3.0 Introduction 33 3.1 The Adem relations 34 v
VI Contents of Volume 1 3.2 The action of A 2 on P(n) 37 3.3 Symmetric functions and blocks 40 3.4 The admissible basis of A 2 44 3.5 The Milnor basis of A 2 46 3.6 Remarks 52 Products and conjugation in A 2 54 4.0 Introduction 54 4.1 The Milnor product formula 54 4.2 The Bullett-Macdonald identity 59 4.3 Conjugation in A 2 61 4.4 Conjugation and the Milnor basis 64 4.5 Remarks 66 Combinatorial structures 67 5.0 Introduction 67 5.1 Sequences, blocks and partitions 69 5.2 Dominance 74 5.3 Binary partitions 76 5.4 Minimal spikes 79 5.5 Spike partitions 82 5.6 Maximal spikes 84 5.7 Dominance in A 2 86 5.8 The excess function on A 2 91 5.9 Remarks 93 The cohit module Q(n) 96 6.0 Introduction 96 6.1 Steenrod and matrix actions on blocks 97 6.2 Filtrations of Q d (n) 100 6.3 Concatenation of blocks 103 6.4 Splicing 107 6.5 The Kameko maps 109 6.6 The duplication map 111 6.7 Tail sequences 114 6.8 Head sequences 116 6.9 Tail and head modules 118 6.10 Remarks 122 Bounds for dim Q d (n) 123 7.0 Introduction 123 7.1 The boundedness theorem 124
?vii 127 132 135 138 139 139 139 146 151 159 162 164 164 165 168 170 174 177 180 182 184 186 187 189 189 191 193 195 196 198 203 206 210 211 211 212 218 221 Contents of Volume 1 7.2 Combinatorial splicing 7.3 Semi-standard blocks 7.4 Young tableaux 7.5 Remarks Special blocks and a basis for Q(3) 8.0 Introduction 8.1 Blocks with large head 8.2 Blocks with long tail 8.3 A monomial basis of 0^(3) 8.4 Blocks of head length n — 1 8.5 Remarks The dual of the hit problem 9.0 Introduction 9.1 The divided power algebra DP(n) 9.2 The action of matrices on DP(n) 9.3 Down squares Sq* 9.4 The Steenrod kernel K(n) 9.5 Dual Kameko and duplication maps 9.6 Tail and head sequences for DP(n) 9.7 Dual tail modules 9.8 Dual head modules 9.9 K d (3) for if = 2* — 1 9.10 Remarks K(3) and Q(3) as F 2 GL (3)-modules 10.0 Introduction 10.1 Some irreducible F 2 GL(n)-modules 10.2 Transpose duality 10.3 K d (3) for d = 2 I+I 10.4 K d (3) for d = (2 5+t — 1)4- (2 — 1) 10.5 The flag module FL(3) 10.6 K rf (3) and Q d (3) as F2GL(3)-modules 10.7 Submodules of Q d (3) 10.8 Remarks The dual of the Steenrod algebra 11.0 Introduction 11.1 Hopf algebras 11.2 The coproduct A 2 -*? A 2 ® A 2 11.3 The Hopf algebra structure of A 2
Contents of Volume 1 viii 11.4 Duality for Hopf algebras 223 11.5 The dual algebra AJ 226 11.6 Conjugation in the Milnor basis 229 11.7 Remarks 233 12 Further structure of A 2 234 12.0 Introduction 234 12.1 Some conjugation formulae 235 12.2 The Milnor elements Sqft 237 12.3 The subalgebras A q ,q = 2‘ 240 12.4 The subalgebras A 2 (A.) 243 12.5 2-atomic numbers and bases 246 12.6 The Amon C basis 251 12.7 Remarks 252 13 Stripping and nilpotence in A 2 254 13.0 Introduction 254 13.1 Cap products for Hopf algebras 255 13.2 The action of A^ on A 2 257 13.3 The halving map of A 2 260 13.4 The odd subalgebra Od 262 13.5 Nilpotence of Sq 2 * 266 13.6 Relations in A ? 269 13.7 Nilpotence of Pj 275 13.8 Remarks 278 14 The 2-dominance theorem 279 14.0 Introduction 279 14.1 Hie excess theorem 280 14.2 Stripping and conjugation for ix{d) = 1 282 14.3 The numerical function y 285 14.4 Stripping and conjugation for general d 287 14.5 Proof of the excess theorem 292 14.6 Xq lkvi] in the Milnor basis 294 14.7 Remarks 296 Ï5 Invariants and the hit problem 297 15.0 Introduction 297 15.1 Dickson invariants 298 15.2 The hit problem for D(2) 302 15.3 The action of A 2 on Dickson invariants 303 15.4 The hit problem for P(2) H2 308
Contents of Volume 1 IX 15.5 The hit problem for P(3) H3 311 15.6 The relative hit problem for D(3) 316 15.7 Elementary Dickson monomials 318 15.8 The relative hit problem for D(n) 320 15.9 Remarks 322 Bibliography 325 Index of Notation for Volume 1 337 Index for Volume 1 339 Index of Notation for Volume 2 343 Index for Volume 2 345
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| isbn | 9781108414487 |
| language | English |
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| spelling | Walker, Grant Verfasser (DE-588)1145076750 aut Polynomials and the mod 2 Steenrod algebra Volume 1 The Peterson hit problem Grant Walker (University of Manchester), Reginald M. W. Wood (University of Manchester) Cambridge Cambridge University Press 2018 xxiv, 346 Seiten txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 441 London Mathematical Society lecture note series Steenrod-Algebra (DE-588)4182999-2 gnd rswk-swf Steenrod-Algebra (DE-588)4182999-2 s DE-604 Wood, Reginald M. W. Verfasser (DE-588)1145076998 aut (DE-604)BV044714180 Volume 1 London Mathematical Society lecture note series 441 (DE-604)BV000000130 441 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030110720&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Walker, Grant Wood, Reginald M. W. Polynomials and the mod 2 Steenrod algebra London Mathematical Society lecture note series Steenrod-Algebra (DE-588)4182999-2 gnd |
| subject_GND | (DE-588)4182999-2 |
| title | Polynomials and the mod 2 Steenrod algebra |
| title_auth | Polynomials and the mod 2 Steenrod algebra |
| title_exact_search | Polynomials and the mod 2 Steenrod algebra |
| title_full | Polynomials and the mod 2 Steenrod algebra Volume 1 The Peterson hit problem Grant Walker (University of Manchester), Reginald M. W. Wood (University of Manchester) |
| title_fullStr | Polynomials and the mod 2 Steenrod algebra Volume 1 The Peterson hit problem Grant Walker (University of Manchester), Reginald M. W. Wood (University of Manchester) |
| title_full_unstemmed | Polynomials and the mod 2 Steenrod algebra Volume 1 The Peterson hit problem Grant Walker (University of Manchester), Reginald M. W. Wood (University of Manchester) |
| title_short | Polynomials and the mod 2 Steenrod algebra |
| title_sort | polynomials and the mod 2 steenrod algebra the peterson hit problem |
| topic | Steenrod-Algebra (DE-588)4182999-2 gnd |
| topic_facet | Steenrod-Algebra |
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