Singular fibers of stable maps and signatures of 4–manifolds

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Cobordisms of Fold Maps of 4-manifolds into the Space

We compute the oriented cobordism group of fold maps of 4-manifolds into R 3 with all the possible restrictions (and also with no restriction) to the singular fibers. We also give geometric invariants which describe completely the cobordism group of fold maps.

Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs

We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of 3–manifolds into the plane. Furthermore, we show that certain cohomology classes associated with the universal complexes of singular fibers give complete invariants f...

Pontryagin-thom-szűcs Type Construction for Non-positive Codimensional Singular Maps with Prescribed Singular Fibers

We give a Pontryagin-Thom-Szűcs type construction for non-positive codimensional singular maps, and obtain results about cobordism and bordism groups of −1 codimensional stable maps with prescribed singular fibers.

Gradient estimates and blow - up analysis for stationary harmonic maps

For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not carry any harmonic S2, then the singular sets of stationary maps are m ≤ n− 4 rectifiable. Both of these results follow from a general analys...