mapping space

# Contents

## Idea

The result of evaluation fibration of mapping spaces extends to more general evaluation maps between mapping spaces. One way to interpret that result is that the inclusion ${C}^{\infty }\left(S,p;M,q\right)\to {C}^{\infty }\left(S,M\right)$ has a tubular neighbourhood. Providing $M$ has enough diffeomorphisms, this is true of more general inclusions where they are defined by “coincidences”. That is to say, if $P$ is a condition on maps $S\to M$ that prescribes where certain points “coincide”, then the submanifold of ${C}^{\infty }\left(S,M\right)$ of smooth maps satisfying this condition will have a tubular neighbourhood in the manifold of all smooth maps.

Revised on June 3, 2011 08:56:31 by Urs Schreiber (89.204.137.115)