nLab
tubular neighbourhood of a 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 (S,p;M,q)C (S,M)C^\infty(S,p;M,q) \to C^\infty(S,M) has a tubular neighbourhood. Providing MM has enough diffeomorphisms, this is true of more general inclusions where they are defined by “coincidences”. That is to say, if PP is a condition on maps SMS \to M that prescribes where certain points “coincide”, then the submanifold of C (S,M)C^\infty(S,M) 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)