Prove that the maps that send to the block matrices and are homotopic.

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#
homotopy theory

# Homotopic maps in the general linear group

# Stable equivalence

Prove that the maps that send to the block matrices and are homotopic.

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Given a topological space we can construct its suspension . This construction can be lifted to a functor from topological spaces to topological spaces that acts on arrows by sending a continuous map to its suspension which is just in each “level” of the suspensions.

*Problem 1: *Find two continuous non homotopic maps such that their suspensions are homotopy equivalent.

*Problem 2:* Find a non nullhomotopic map such that its suspension is nullhomotopic, but now we require the domain and the codomain to be connected!