Stable Diffeomorphism Groups of 4-manifolds

Characteristic Cohomotopy Classes for Families of 4-manifolds

Families of smooth closed oriented 4-manifolds with a complex spin structure are studied by means of a family version of the Bauer-Furuta invariants. The definition is given in the context of parametrised stable homotopy theory, but an interpretation in terms of characteristic cohomotopy classes on Thom spectra associated to the classifying spaces of complex spin diffeomorphism groups is given ...

A polynomial invariant of diffeomorphisms of 4–manifolds

We use a 1–parameter version of gauge theory to investigate the topology of the diffeomorphism group of 4–manifolds. A polynomial invariant, analogous to the Donaldson polynomial, is defined, and is used to show that the diffeomorphism group of certain simply-connected 4–manifolds has infinitely generated π0 . AMS Classification 57R52; 57R57

Stable Exponentially Harmonic Maps Between Finsler Manifolds

A diffeomorphism classification of manifolds which are like projective planes

We give a complete diffeomorphism classification of 1-connected closed manifolds M with integral homology H∗(M) ∼= Z ⊕ Z ⊕ Z, provided that dim(M) 6= 4. The integral homology of an oriented closed manifold1 M contains at least two copies of Z (in degree 0 resp. dimM). IfM is simply connected and its homology has minimal size (i.e., H∗(M) ∼= Z⊕Z), then M is a homotopy sphere (i.e., M is homotopy...

Diffeomorphism Groups of Reducible 3 Manifolds

We introduce here a more compact variant of constructions of César de Sá-Rourke and Hendriks-Laudenbach measuring the difference between the homotopy type of the diffeomorphism group of a reducible 3-manifold and the homotopy types of the diffeomorphism groups of its prime factors. This allows us to prove some interesting cases of a conjecture of Kontsevich which asserts that the classifying sp...