Stably diffeomorphic manifolds and the realisation of modified surgery obstructions

2021/09/12 by Anthony Conway, Diarmuid Crowley, Conway, Anthony +5
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2109.05632

Abstract

For every k ≥ 2 we construct infinitely many 4k-dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In fact we construct infinitely many such infinite sets. To achieve this we prove a realisation result for appropriate subsets of Kreck's modified surgery monoid ℓ_2q+1(ℤ[π]), analogous to Wall's realisation of the odd-dimensional surgery obstruction L-group L_2q+1^s(ℤ[π]).

Related

• Stably diffeomorphic manifolds and l_2q+1(Z[π])
• Extended surgery theory for simply-connected 4k-manifolds
• Stable equivalence relations on 4-manifolds
• 4-manifolds, surgery on loops and geometric realization of Tietze transformations
• Stable classification of 4-manifolds obtained by the surgery on loops