On the Finiteness of the Image of Unstable Hurewicz Homomorphism

2018-08-07 15:00 - 2018-08-07 16:00 Room 9, Quan Zhai, BICMR Abstract. We consider loop spaces $\\Omega^i\\Sigma^iX$ and the problem of determining spherical classes in their Z\/2-homology. If X is a Thom complex, then the problem is related to the bordism of immersions through results of Thom and Koschorke-Sanderson. We prove that if $X$ satisfies some specific conditions on its cell-structure then there are only finitely many spherical classes in the homology of the aforementioned loop spaces. This implies that above a dimension, all immersions of some specific types are bordant to a boundary. We shall also discuss the relations of these results to conjectures of Eccles and Curtis on the homology of (free) infinite loop spaces which have been a starting\/motivating point for the present work.<\/span>