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A real world example of a diffrent topology is is a dress whose straps intercect with one wrapping around the other so they from an X on someones back.

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It sounds like you are describing a racerback:

http://www.zadehome.com/images/product/Racerback_Nightie_2_M...

But I think that falls into the category of "sack with a couple more holes".

That picture is a "sack with a couple more holes" however if rather than cloth connecting the straps they tied together in a knot. In that case the knot is a topologically distant feature which is maintained regardless how you deform the garment.

I can't find a picture of it. However while this is still a "sack with a couple more holes" http://s7.kmart.com/is/image/Sears/049B018579550001?hei=500&... if you picture having that strap be wrapped around at the point of intersection it can still be unwound. However, if you form a slip knot at the intersection it can not be removed by deforming the garment.

I think you are correct. My mistake, I didn't properly visualize what you were describing.

I can't visualise what you've described, can you give an example?

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