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I got a question by email about the equivariant tubular neighbourhoods in loop spaces (as opposed to those defined using propagating flows so I figured it was time to nLabify that section of differential topology of mapping spaces. Of course, in so doing I figured out a generalisation: given a fibre bundle $E \to B$, everything compact, we consider smooth maps $E \to M$ which are constant on fibres. This is a submanifold of the space of all smooth maps $E \to M$. Assuming we can put a suitable measure on the fibres of $E$, then we can define a tubular neighbourhood of this submanifold.
Details at equivariant tubular neighbourhoods. Title may be a bit off now, but itâ€™s that because the original case was for the fibre bundle $S^1 \to S^1$ with fibre $\mathbb{Z}_n$.
This entry is also notable because I produced it using a whole new LaTeX-to-iTeX converter. Details on the relevant thread.
The displayed equation above lemma 1 (in version 1) is a bit wonky on the spacing, but apart from that a quick scan showed it to be very nice. Well done!
Aagh. I keep forgetting that \text
behaves ever so slightly differently with regard to swallowing spaces. Fixed.
Also added a picture to try to illustrate some of the maps.
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