2024/09/04 by Csaba L. Nagy, Nagy, Csaba, John W. Nicholson +3
Mathematics · #57N65 #57Q10 (Primary) 19J10 (Secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2409.03082
openalex publication_date 2024/09/04 · openalex created_date 2024/10/19 · openalex updated_date 2026/07/28
We characterise the set of fundamental groups for which there exist n-manifolds that are h-cobordant (hence homotopy equivalent) but not simple homotopy equivalent, when n is sufficiently large. In particular, for n ≥ 12 even, we show that examples exist for any finitely presented group G such that the involution on the Whitehead group Wh(G) is nontrivial. This expands on previous work, where we constructed the first examples of even-dimensional manifolds that are homotopy equivalent but not simple homotopy equivalent. Our construction is based on doubles of thickenings, and a key ingredient of the proof is a formula for the Whitehead torsion of a homotopy equivalence between such manifolds.