A woman I saw yesterday had styled her hair in a Klien bottle fashion. It came down into a single thick strand that swirled about her head and then became neatly incorporated into the rest of her hair.
I asked her about her hair and she said "It takes TIME to make all of my hair to touch all the rest of my hair."
I said "thank you for solving a cosmological question."

This may only solve problems of the shape of the universe on a locality basis but it does not require any addition of dimensions nor does it reduce dimensions down to only two.

The model of two layers of 3 dimensional space hovering adjacent to one another (Brane Theory) still remains viable.

More hairstyle research is needed.