Algebraic criteria for stable diffeomorphism of spin 4-manifolds / Daniel Kasprowski, Mark Powell, Peter Teichner.

Format:

Book

Author/Creator:

Kasprowski, Daniel, 1986- author.

Powell, Mark, (Mathematician), author.

Teichner, Peter, author.

Series:

Memoirs of the American Mathematical Society ; vol. 312, number 1579 (first of 7 numbers)

Memoirs of the American Mathematical Society, 0065-9266 ; volume 312, number 1579 (August 2025)

Language:

English

Subjects (All):

Diffeomorphisms.

Physical Description:

v, 98 pages : illustrations ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2025.

Summary:

We study closed, connected, spin 4-manifolds up to stabilisation by connected sums with copies of S² x S². For a fixed fundamental group, there are primary, secondary and tertiary obstructions, which together with the signature lead to a complete stable classification. The primary obstruction exactly detects CP² stable diffeomorphism and was previously related to algebraic invariants by Kreck and the authors. In this article we formulate conjectural relationships of the secondary and tertiary obstructions with algebraic invariants: the secondary obstruction should be determined by the (stable) equivariant intersection form and the tertiary obstruction via a -invariant recording intersection data between 2-spheres, with trivial algebraic self-intersection, and their Whitney discs. We prove our conjectures for the following classes of fundamental groups: groups of cohomological dimension at most 3, right-angled Artin groups, abelian groups, and finite groups with quaternion or abelian 2-Sylow subgroups. We apply our theory to give a complete algebraic stable classification of spin -manifolds with fundamental group Z x Z/2.

Contents:

Chapter 1. Introduction

Chapter 2. Background - Chapter 3. The secondary obstruction

Chapter 4. The tertiary obstruction

Chapter 5. Inheritance results

Chapter 6. Examples

Chapter 7. The stable classification for fundamental group Z x Z/2

Bibliography.

Notes:

"August 2025, volume 312, number 1579 (first of 7 numbers)"

Includes bibliographic references (pages 97-98).

ISBN:

9781470475338

1470475332

OCLC:

1535710883