Four-manifolds, two-complexes and the quadratic bias invariant

Autor:	Hambleton, Ian, Nicholson, John
Rok vydání:	2024
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Topology 57K41 57N65 20F05 55U15 57R67
Druh dokumentu:	Working Paper
Popis:	Kreck and Schafer produced the first examples of stably diffeomorphic closed smooth 4-manifolds which are not homotopy equivalent. They were constructed by applying the doubling construction to 2-complexes over certain finite abelian groups of odd order. By extending their methods, we formulate a new homotopy invariant on the class of 4-manifolds arising as doubles of 2-complexes with finite fundamental group. As an application we show that, for any $k \ge 2$, there exist a family of $k$ closed smooth 4-manifolds which are all stably diffeomorphic but are pairwise not homotopy equivalent. Comment: 43 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.15089 Zobrazit plný text záznamu View this record from Arxiv