Ganesh Ujwal
New member
- Joined
- Aug 10, 2014
- Messages
- 32
Let \(\displaystyle K\) denote a simplicial complex and [/tex]Y[/tex] some topological space. Let us also denote by \(\displaystyle K^n\) the \(\displaystyle n\)-skeleton of \(\displaystyle K\). I would like to have an example for the following situation:
There is a map \(\displaystyle f^1:K^1\to Y\) that can be extended to \(\displaystyle f^2:K^2\to Y\) and yet no such extension can be further extended to \(\displaystyle f^3:K^3\to Y\).
The idea is that there is an obstruction to the existence of \(\displaystyle f^3\) already on the one-dimensional level but not by obstructing the existence of \(\displaystyle f^2\). It is written in Hilton and Wylie's book that it is possible, yet I was not able to construct an explicit example myself.
There is a map \(\displaystyle f^1:K^1\to Y\) that can be extended to \(\displaystyle f^2:K^2\to Y\) and yet no such extension can be further extended to \(\displaystyle f^3:K^3\to Y\).
The idea is that there is an obstruction to the existence of \(\displaystyle f^3\) already on the one-dimensional level but not by obstructing the existence of \(\displaystyle f^2\). It is written in Hilton and Wylie's book that it is possible, yet I was not able to construct an explicit example myself.