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Thomas C. — Characteristic Classes and the Cohomology of Finite Groups
Thomas C. — Characteristic Classes and the Cohomology of Finite Groups

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Название: Characteristic Classes and the Cohomology of Finite Groups

Автор: Thomas C.

Аннотация:

The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general results for the integral cohomology ring of a group G of prime power order. Among the groups considered are those of p-rank less than 3, extra-special p-groups, symmetric groups and linear groups over finite fields. An important tool is the Riemann - Roch formula which provides a relation between the characteristic classes of an induced representation, the classes of the underlying representation and those of the permutation representation of the infinite symmetric group. Dr Thomas also discusses the implications of his work for some arithmetic groups which will interest algebraic number theorists. Dr Thomas assumes the reader has taken basic courses in algebraic topology, group theory and homological algebra, but has included an appendix in which he gives a purely topological proof of the Riemann - Roch formula.


Язык: en

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 144

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Omega$-spectrum      115
(co)induced      2
Adams operations      54
Adams, J.F.,      xi 118
Algebraic integers      85
Augmentation ideal, $I_G$      9
Automorphism group, Aut(G)      7
Bernoulli numbers      80
Blackburn, N.,      xi 95
Blackburn’s Theorem      95
Blichfeldt’s Theorem      53
Brauer lifting      109
Brauer’s Theorem      52
Bundle, coordinate      56
Bundle, defined by a representation      57
Bundle, direct image      67
Bundle, flat      64
Bundle, induced      57
Bundle, vector      57
Burnside, W.      122
Centraliser, $Z_K$, $Z_p$      28 92 103
CHARACTER      50
Character table of $SL(2, \mathbb{F}_q)$      103
Character, virtual      51
Charlap, L., & Vasquez, A.      48
Chern character      117
Chern classes of bundles      60
Chern ring      71
Class function      50
Classifying spaces for finite groups      65
Classifying spaces for topological groups      62
Coboundary homomorphism      4
Cohomological extension      3
Cohomological p-period      32 92
Cohomology equivariant      107
Cohomology groups      3
Cohomology operations      116
Cohomology periodic      6 31
Coinvariant elements      8
Compatible pair      19
Conjugation      20
Connecting homomorphism      3
Connective k-theory      115
Corestriction      20
Crossed homomorphism      6
Crossed homomorphism, principal      6
Cup product      17
Detecting family of subgroups      108
Diagonal subgroup      102 109 113
Dimension shifting      4 20 23 42
Double coset      25
Double coset formula      25
Duality      29
Eckmann — Shapiro Lemma      20
Eckmann, B.,      xi 20 86
Edge homomorphism      39 41
Elementary subgroup      52
Euler class      61
Evens, L., & Kahn, D.      69 90
Extension      7 13
Extension, central      76
Factor systems      6
Farrell, T.      12
Field, cyclotomic      86
Field, exceptional      86
Field, quadratic      87
Frobenius automorphism      103
Frobenius reciprocity      23 52
Galois invariance      81 86-8
Global cohomological period      35
Grassmann manifold      62
Grothendieck topologies      88
Grothendieck, A.      87 111
Group of order $p^3$      7 46 99 120-1
Group of order $p^4$      8 13 122
Group, alternating, $A_4$      100
Group, binary dihedral, $D_{4t}^{\ast}$      34
Group, differential graded abelian      39
Group, dihedral, $D_{2^a}$      47
Group, extra special      75
Group, extra special 2-group      77
Group, general linear (over $\mathbb{F}_q$)      104
Group, generalised quaternion      34
Group, minimal non-abelian      63
Group, p-normal      36
Group, p-solvable      95
Group, semidihedral      106
Group, special linear, $SL(3, \mathbb{F}_q)$      xi 106
Group, special linear, over $\mathbb{F}_q$      102
Group, special linear, over $\mathcal{O}$      85
Group, split metacyciic      43 46 74
Group, supersolvable      53
Group, symmetric, $S_n$      79
Group, Weyl      110
Groupring      1
Herbrand quotient      36
Homology groups      8
Inflation      19
Inflation restriction exact sequence      42
Invariant elements      1
J-homomorphism      89
Kuo, T.N.      73
l-adic classes      88
Lewis, G.      48 99 120
Line bundle      58
Localisation (at fixed point set)      107
Mislin, G.      86
Modular characteristic classes      110 111—112
Newton polynomial      54
Norm homomorphism      9
Normal p-rank      95
Normaliser, $N_K$, $N_p$      28 92 103
Outer automorphism, Out(G)      13
p-generator      32
p-rank      91
Pontrjagin class      110
Quillen, D.,      xi 77 89 110
Representation module      49
Representation, cuspidal      104
Representation, direct image      67 ’
Representation, exterior powers of      54
Representation, induced      52
Representation, modular      111
Representation, regular      51
Representation, restricted      52
Resolution      3
Resolution, complete      11
Resolution, free      5
Resolution, standard      4
Restriction      19
Riemann — Roch formulae      69 96—97 114ff
Singer cycle      105
Spectral sequence      43—45 96—99 107—108
Spectral sequence, Lyndon — Hochschild — Serrc      41ff
Splitting principle      58 68
Stable elements      26
Steenrod algebra      118
Stiefel — Whitney class      61 77 110
Swan, R.G.      28 36 52 93
Swan’s Lemma      28
Tate cohomology      10
Total Chern class      60
Transfer of bundles      66
Transfer of representation      52
Transfer, abstract      115
Transfer, cohomological      21
Transgression      42
Universal coboundaries      38
Universal cycles      38
Virtually finite cohomological dimension      11
Wall, C.T.C.      46
Whitney sum      58
Wreath product      66 97 106—107
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