On the homotopy theory of equivariant automorphism groups.
This paper reports on some results concerning:a) The homotopy type of the group of diffeomorphisms of a differentiable compact manifold (with -topology).b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo (with -topology). As a biproduct, one gets new facts about the homotopy groups of , and about the number of connected components of the space of topological and combinatorial pseudoisotopies.The results are contained in Section 1 and Section...
[For the entire collection see Zbl 0699.00032.] A new cohomology theory suitable for understanding of nonlinear partial differential equations is presented. This paper is a continuation of the following paper of the author [Differ. geometry and its appl., Proc. Conf., Brno/Czech. 1986, Commun., 235-244 (1987; Zbl 0629.58033)].
Given a closed 4-manifold M, let M* be the simply-connected 4-manifold obtained from M by killing the fundamental group. We study the relation between the intersection forms λM and λM*. Finally some topological consequences and examples are described.
The Kauffman-Harary conjecture is a conjecture for Fox's colorings of alternating knots with prime determinants. We consider a conjecture for Alexander quandle colorings by referring to the Kauffman-Harary conjecture. We prove that this new conjecture is true for twist knots.