Removing coincidences of maps between manifolds of different dimensions

Removing Coincidences of Maps between Manifolds of Different Dimensions

We consider sufficient conditions of local removability of coincidences of maps f, g:N →M , where M , N are manifolds with dimensions dimN ≥ dimM . The coincidence index is the only obstruction to the removability for maps with fibers either acyclic or homeomorphic to spheres of certain dimensions. We also address the normalization property of the index and coincidence-producing maps.

1 5 O ct 2 00 2 Removing Coincidences of Maps Between Manifolds of Different Dimensions

We consider sufficient conditions of local removability of coincidences of maps f, g : N → M, where M, N are manifolds with dimensions dimN ≥ dimM. The coincidence index is the only obstruction to the removability for maps with fibers either acyclic or homeomorphic to spheres of certain dimensions. We also address the normalization property of the index and coincidence-producing maps.

Removing Coincidences of Maps Between Manifolds With Positive Codimension

We consider obstructions to the removability of coincidences of maps f, g : N → M, where M, N are manifolds with the codimension dimN − dimM ≥ 0. The coincidence index is the only obstruction for maps to surfaces (any codimension) and maps with fibers homeomorphic to 4-, 5-, or 12-dimensional spheres, for large values of dimM.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Lefschetz Coincidence Theory for Maps Between Spaces of Different Dimensions

For a given pair of maps f, g : X → M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism Λfg : H(X) → H(M) of degree (−n). We prove a Lefschetztype coincidence theorem: if the Lefschetz homomorphism is nontrivial then there is an x ∈ X such that f(x) = g(x).