Year: 2025
Type: article
Abstract: We consider the role of the Kervaire--Milnor invariant in the classification of closed, connected, spin 4-manifolds, typically denoted by $M$, up to stabilisation by connected sums with copies of $S^2 \times S^2$. This stable classification is detected by a spin bordism group over the classifying space $Bπ$ of the fundamental group. Part of the computation of this bordism group via an Atiyah--Hirzebruch spectral sequence is determined by a collection of codimension two Arf invariants. We show that these Arf invariants can be computed by the Kervaire--Milnor invariant evaluated on certain elements of $π_2(M)$. In particular this yields a new stable classification of spin $4$-manifolds with 2-dimensional fundamental groups, namely those for which $Bπ$ admits a finite 2-dimensional CW-complex model.
Source: Tunisian Journal of Mathematics
Authors: Daniel Kasprowski, Mark Powell, Peter Teichner
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3164741940