- #1

cianfa72

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- TL;DR Summary
- Möbius strip fiber bundle defined through 'gluing instructions' between its two charts

Hi,

starting from this (old) thread

Neverthless my doubt is: what about the 2 points in ##S^1## (the base space) not taken in account ? On that points (and for the corresponding fibers) we actually do not define any 'gluing instruction' ?

starting from this (old) thread

I'm a bit confused about the following: the transition function ##ϕ_{12}(b)## is defined just on the intersection ##U_1\cap U_2## and as said in that thread it actually amounts to the 'instructions' to glue together the two charts to obtain the Möbius strip.Fredrik said:But suppose instead that the ##ϕ_{12}(b)## is the identity map on ##F## for all ##b## in ##X##, and the map ##f↦−f## for all ##b## in ##Y##. Then the bundle is a Möbius strip.

Neverthless my doubt is: what about the 2 points in ##S^1## (the base space) not taken in account ? On that points (and for the corresponding fibers) we actually do not define any 'gluing instruction' ?