Automorphisms of manifolds (Q2708386)

The basic objects of the survey are simplicial sets of maps of one kind or another, for example for a manifold \(M\), TOP\((M)\) is the simplicial set whose \(k\)-simplices are homeomorphisms \(M\times\Delta^k\to M\times\Delta^k\) which are the identity on \(\partial M\times\Delta^k\). Also considered are homotopy equivalences, \(h\)-cobordisms, diffeomorphisms, etc. In the first chapter these sets are related to one another by geometric methods. Later chapters apply surgery theory and \(h\)-cobordism theory to describe algebraic models for spaces sharing some features of the manifold \(M\). If \(X_1(M)\subset X_2(M)\) are two automorphism spaces of \(M\) then a comparison theory which compares \(BX_1(M)\) with \(BX_2(M)\) is developed.NEWLINENEWLINEFor the entire collection see [Zbl 0957.00062].