We establish a braid of interlocking exact sequences containing the group of homotopy self-equivalences of a smooth or topological 4-manifold. The braid is computed for manifolds whose fundamental group is finite of odd order.
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The aim of this paper is to give an -cobordism classification of topological -manifolds in terms of the standard invariants using the group of homotopy self-equivalences. Hambleton and Kreck constructed a braid to study the group of homotopy self-equivalences of -manifolds. Using this braid together with the m…
Models for self-equivalences and diffeomorphisms of manifolds.
problem Classifying spaces of self-equivalences and diffeomorphisms of manifolds.
method Construct rational models using equivariant algebraic methods.
result Formula for rational cohomology of classifying spaces.
A pass-move and a $#$-move are local moves on oriented links defined by L.H. Kauffman and H. Murakami respectively. Two links are self pass-equivalent (resp. self $#$-equivalent) if one can be deformed into the other by pass-moves (resp. $#$-moves), where non of them can occur between distinct components of the link. T…
Let y''' = f(x, y, y', y'') be a 3rd order ODE. By Cartan equivalence method, we will study the local equivalence problem under the transformations group of time-fixed coordinates.
We will prove the relative homotopy principle for smooth maps with singularities of a given {\cal K}-invariant class with a mild condition. We next study a filtration of the group of homotopy self-equivalences of a given manifold P by considering singularities of non-negative {\cal K}-codimensions.
We study isomorphism classes of symplectic dual pairs P <- S -> P-, where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres. For fixed P, these Morita self-equivalences of P form a group Pic(P) under a natural `…
Let be a positive integer, and let be square-free odd. We classify the set of equivariant homeomorphism classes of free -actions on the product of spheres, up to indeterminacy bounded in . The description is expressed in terms of number theory. The techniques are various appl…
Finite type and finitely generated homotopy groups for manifold automorphisms.
problem Finite type and homotopy group properties of manifold automorphism spaces.
method Analyzing the classifying space of diffeomorphism groups and using simple homotopy theory.
result The classifying space of diffeomorphism groups has finitely generated homotopy groups.