# TOPOLOGICAL 4-MANIFOLDS WITH 4-DIMENSIONAL FUNDAMENTAL GROUP

@article{Kasprowski2021TOPOLOGICAL4W,
title={TOPOLOGICAL 4-MANIFOLDS WITH 4-DIMENSIONAL FUNDAMENTAL GROUP},
author={Daniel Kasprowski and Markus Land},
journal={Glasgow Mathematical Journal},
year={2021},
volume={64},
pages={454 - 461}
}
• Published 7 July 2020
• Mathematics
• Glasgow Mathematical Journal
Abstract Let $\pi$ be a group satisfying the Farrell–Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$ has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby–Siebenmann invariant. If $\pi$ is good in the sense of Freedman, it follows that two such…
2 Citations
Gluck twists on concordant or homotopic spheres
• Mathematics
• 2022
. Let M be a compact 4-manifold and let S and T be embedded 2-spheres in M , both with trivial normal bundle. We write M S and M T for the 4-manifolds obtained by the Gluck twist operation on M along
Homotopy ribbon discs with a fixed group
In the topological category, the classification of homotopy ribbon discs is known when the fundamental group G of the complement is Z and the Baumslag-Solitar group BS(1, 2). We prove classification

## References

SHOWING 1-10 OF 33 REFERENCES
Topological rigidity for non-aspherical manifolds
• Mathematics
• 2005
The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the
4-Manifold topology I: Subexponential groups
• Mathematics
• 1995
The technical lemma underlying the 5-dimensional topologicals-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating π1-null
Surgery and duality
Surgery, as developed by Browder, Kervaire, Milnor, Novikov, Sullivan, Wall and others is a method for comparing homotopy types of topological spaces with difieomorphism or homeomorphism types of
TOPOLOGICAL 4-MANIFOLDS WITH GEOMETRICALLY TWO-DIMENSIONAL FUNDAMENTAL GROUPS
• Mathematics
• 2008
Closed oriented 4-manifolds with the same geometrically two-dimensional fundamental group (satisfying certain properties) are classified up to s-cobordism by their w2-type, equivariant intersection
A survey of 4-manifolds through the eyes of surgery
• Mathematics
• 1998
Surgery theory is a method for constructing manifolds satisfying a given collection of homotopy conditions. It is usually combined with the s{cobordism theorem which constructs homeomorphisms or
Stable classification of 4‐manifolds with 3‐manifold fundamental groups
• Mathematics
• 2015
We study closed, oriented 4‐manifolds whose fundamental group is that of a closed, oriented, aspherical 3‐manifold. We show that two such 4‐manifolds are stably diffeomorphic if and only if they have
The topology of four-dimensional manifolds
0. Introduction Manifold topology enjoyed a golden age in the late 1950's and 1960's. Of the mysteries still remaining after that period of great success the most compelling seemed to lie in
Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory.
• Mathematics
• 1998
We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraic K- and L-theory of integral group rings and to the Baum-Connes Conjecture on the topological K-theory of