Year: 2020
Type: preprint
Abstract: In this paper we isolate a general Universal Coefficient Theorem in the context of abelian categories. We then apply it in the left heart of the quasi-abelian category of abelian Polish groups to obtain short exact sequences relating Steenrod homology and Čech cohomology, regarded as functors to such a category. These are then used to (1) intrinsically characterize the phantom subgroups of Čech cohomology via a recursive purely algebraic formula, which can be see as a higher order generalization of the Milnor exact sequence; (2) describe phantom subgroups of Čech cohomology in terms of higher order phantom maps, in the context of the homotopical description of Čech cohomology; (3) classify up to homotopy (phantom) maps on higher order versions of solenoid complements, and measure from the viewpoint of Borel complexity theory the complexity of such a classification problem.
Source: arXiv (Cornell University)
Authors: Caputi, Luigi, Lupini, Martino
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1290427602, G2735103206
OpenAlex ID: W3088137403