Hyperbolic actions and 2nd bounded cohomology of subgroups of Out(Fn) / Michael Handel, Lee Mosher.

Format:

Book

Author/Creator:

Handel, Michael, 1949- author.

Mosher, Lee, 1957- author.

Series:

Memoirs of the American Mathematical Society ; v. 1454.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1454.

Language:

English

Subjects (All):

Group theory.

Physical Description:

v, 170 pages : illustrations ; 26 cm.

Other Title:

Hyperbolic actions and second bounded cohomology of subgroups of Out(Fn)

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

"In this two part work we prove that for every finitely generated subgroupΓ < Out(Fn), either Γ is virtually abelian or H2b (Γ; R) contains a vector space embedding of 1. The method uses actions on hyperbolic spaces. In Part I we focus on the case of infinite lamination subgroups Γ--those for which the set of all attracting laminations of all elements of Γ is an infinite set--using actions on free splitting complexes of free groups. In Part II we focus on finite lamination subgroups Γ and on the construction of useful new hyperbolic actions of those subgroups." -- Provided by publisher

Contents:

Part 1. Infinite lamination subgroups

Introduction

Background material

Reducing Theorem A to Theorem C and the WWPD Construction

Well functions and weak tiling functions

Proof of the WWPD Construction Theorem

Part 2. Finite lamination subgroups

Lifting to an automorphism group

Hyperbolic Action Theorem, Multi-edge case: introduction

Flaring in a top EG stratum

Flaring in T* and hyperbolicity of S

Abelian subgroups of Out (Fn)

A train track semigroup action

The suspension action

Notes:

"December 2023, volume 292, number 1454 (fourth of 6 numbers)."

Includes bibliographical references (pages 167-170).

ISBN:

1470466988

9781470466985

OCLC:

1416950861