pith. sign in

arxiv: 0907.0308 · v5 · pith:FISONX4Enew · submitted 2009-07-02 · 🧮 math.GT · math.AT

Homotopy invariance of 4-manifold decompositions: connected sums

classification 🧮 math.GT math.AT
keywords assumingconjectureconnecteddecompositionsfundamentalgrouphomotopyborel
0
0 comments X
read the original abstract

We show, up to h-cobordism, that the existence and uniqueness of connected sum decompositions of oriented 4-dimensional manifolds is an invariant of homotopy equivalence, assuming that the fundamental group of each summand is "good" in the sense of Freedman and Quinn. On a separate note, we observe that the Borel Conjecture is true in dimension 4 up to s-cobordism, assuming that the fundamental group satisfies the Farrell--Jones Conjecture.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.