Hi all,
I need someone to explain me this one:
Prove that the the mobius band does not retract to its boundary.
It should be a well-known property from what I understand, but I cannot find the proof anywhere. Thanks in advance for your help.
Hi all,
I need someone to explain me this one:
Prove that the the mobius band does not retract to its boundary.
It should be a well-known property from what I understand, but I cannot find the proof anywhere. Thanks in advance for your help.
A Mobius band deformation retracts to its middle circle. Thus, , where M is a Mobius band.
Let B be a boundary circle of a Mobius band. Then is induced by a degree 2 map of its central circle to itself. Thus . We conclude that B cannot be a retract of a Mobius band whose fundamental group is .