Contents

# Contents

## Definition

Given a homotopy theory, i.e. an (infinity,1)-category, then a tower of homotopy fibers or tower of fibrations or similar is a tower diagram of the form

$\array{ \vdots \\ {}^{\mathllap{hofib(f_2)}}\downarrow \\ X_2 &\stackrel{f_2}{\longrightarrow}& A_2 \\ {}^{\mathllap{hofib(f_1)}}\downarrow \\ X_1 &\stackrel{f_1}{\longrightarrow}& A_1 \\ {}^{\mathllap{hofib(f_0)}}\downarrow \\ X &\stackrel{f_0}{\longrightarrow}& A_0 }$

where each hook is a homotopy fiber sequence.

## Properties

The long exact sequences of homotopy groups for each of the hooks in the tower combine to yield an exact couple. The corresponding spectral sequence of an exact couple is a means to (approximately) compute the homotopy groups of the base object $X$ of the tower

## References

Last revised on October 15, 2019 at 05:19:50. See the history of this page for a list of all contributions to it.