Mapping class groups of low genus and their cohomology / D. J. Benson, F. R. Cohen.

Format:

Book

Author/Creator:

Benson, D. J. (David J.), 1955- author.

Cohen, Frederick R. (Frederick Ronald), 1945- author.

Series:

Memoirs of the American Mathematical Society ; Number 443.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 443

Language:

English

Subjects (All):

Low-dimensional topology.

Complexes.

Mappings (Mathematics).

Homology theory.

Physical Description:

1 online resource (113 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1991.

Language Note:

English

Summary:

This book is concerned with the calculation of the cohomology of the mapping class group of a closed oriented surface of genus two. The methods used involve braid groups, modular representations of symmetric groups, and configuration spaces.

Contents:

""Contents""; ""Introduction""; ""Artin's Braid Group and the Homology of Certain Subgroups of the Mapping Class Group""; ""1 Statement of Results""; ""2 Presentations""; ""3 H*(K[sub(n)]; Z)""; ""4 Proof of Theorem 1.1""; ""5 The mod�5 Cohomology of T[sup(0)][sub(2,0)] and T[sup(6)][sub(0,0)]""; ""6 The mod�3 Cohomology of T[sup(0)][sub(2,0)]""; ""7 The mod�2 Cohomology of T[sup(0)][sub(2,0)]; Theorems 1.3 and 1.4""; ""8 H*(Σ[sub(6)]; H*(K[sub(6)]; F[sub(5)])); Theorem 5.3""; ""9 Theorem 1.6""; ""10 Facts about B[sub(n)] and Lemmas 3.2 and 3.3""

""Specht Modules and the Cohomology of Mapping Class Groups""""1 Introduction""; ""2 The modules H[sup(j)(K[sub(n),Z), j â?? 3""; ""3 Modules for A[sub(6)] and Σ[sub(6)] in characteristic two""; ""4 Diagrams for H[sup(j)]; (K[sub(6)],F[sub(2)]) as F[sub(2)]A[sub(6)]â€?modules""; ""5 Calculation of H*(Σ[sub(6)]; ,H*(K[sub(6)],F[sub(2)])) â?? H*(T[sup(6)][sub(0,0)],F[sub(2)])""; ""6 Finite subgroups of T[sup(6)][sub(0,0)] and T[sup(0)][sub(2,0)]""; ""7 Calculation of the spectral sequences for H*(T[sup(6)][sub(0,0,)], F[sub(2)] and H*(T[sup(0)][sub(2,0,)], F[sub(2)]""

""8 Calculations in characteristic three""""The mod 2 cohomology of the mapping class group for a surface of genus two""; ""1 Introduction""; ""2 A construction for K(T[sup(n)[sub(0,00], 1); characteristic classes""; ""3 Steenrod operations on H*(F(S[sup(2)],6)/Σ[sub(6)],F[sub(2)]""; ""4 Steenrod operations on H*(T[sup(6)][sub(0,0)],F[sub(2)]""; ""5 The spectral sequence for T[sup(0)][sub(2,0)]""

Notes:

"March 1991, Volume 90, Number 443 (end of volume)."

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

1-4704-0869-4