Cell-Like Maps and Surgery

TL;DR

This paper demonstrates that for any dimension n≥6 and any number of manifolds m, there exist m non-homeomorphic n-manifolds that can all be mapped onto the same space X via cell-like maps, highlighting complex relationships in high-dimensional topology.

Contribution

It establishes the existence of multiple non-homeomorphic manifolds sharing a common cell-like image, extending understanding of manifold mappings in high dimensions.

Findings

Existence of m non-homeomorphic n-manifolds for n≥6 mapping onto the same space

Cell-like maps can relate distinct high-dimensional manifolds

Results apply to arbitrary m and fixed n≥6

Abstract

We show that for any $n\geq6$, for any $m$, we can find $m$ non-homeomorphic $n$-manifolds that can be mapped by cell-like maps onto the same space $X$.