On the Finiteness of the Image of Unstable Hurewicz Homomorphism
Time: 2018-07-27
Published By: Meng Yu
Speaker(s): Hadi Zare (University of Tehran)
Time: 15:00-16:00 August 7, 2018
Venue: 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.
