62 research outputs found
The local defect index up to finite ambiguity
The rational Hopf invariant of the primary obstruction to
a nowhere vanishing section in a vectorbundle is computed in terms of
characteristic classes. This leads to a local rigidity result on the local
defect index of a map
Tension field and Index form of Energy-Type Functionals
We derive variational formulae for natural first order energy function-
als and obtain criteria for the stability of isometric immersions. This
generalizes known results for the classical energy, the p-energy and the
exponential energ
Homotopy classes with small Jacobians
If the infimum of the conformal k-Jacobian on the homotopy class of
a map between compact Riemannian manifolds vanishes then the map
factors rationally through the k-skeleton of the target manifold
Stability of natural energy functionals at Riemannian subimmersions
We derive variational formulas of natural first order functionals and obtain
criteria for stability in particular at Riemannian subimmersions
The local defect index up to finite ambiguity
The rational Hopf invariant of the primary obstruction to
a nowhere vanishing section in a vectorbundle is computed in terms of
characteristic classes. This leads to a local rigidity result on the local
defect index of a map
The Global Defect Index
We show how far the local defect index determines the behaviour of
an ordered medium in the vicinity of a defect
Manifolds Carrying Large Scalar Curvature
Let W = S
E be a complex spinor bundle with vanishing first Chern
class over a simply connected spin manifold M of dimension 5. Up to
connected sums we prove that W admits a twisted Dirac operator with
positive order-0-term in the Weitzenb¨ock decomposition if and only if
the characteristic numbers Aˆ(TM)[M] and ch (E)Aˆ(TM)[M] vanish.
This is achieved by generalizing [2] to twisted Dirac operators
Bordism of regularly defective maps
To a topological space V we assign the bordism group Ndef
n (V ) of reg-
ularly defective maps f : M◦→V on closed n-dimensional manifolds M.
These are triples (M,, f) where is a closed submanifold ⊂ M and
f a continuous map f : M r → V .
We briefly review the construction of the defect complex DV given by
M. Rost in [17] and show that Ndef
n (V ) is isomorphic to ordinary bordism
Nn(DV ). The bordism classes in Ndef
n (V ) ∼= Nn(DV ) are detected by
characteristic numbers twisted with cohomology classes of DV . Some of
these numbers can be described without reference to the defect complex.
As an example we treat the case of the circle V = S1. We compute
Ndef
n (S1), construct a basis and a complete set of characteristic numbers
An Integral Formula for the Maslov-Index of a Symplectic Path
The Maslov index of a not necessarily closed path M in the symplectic
group Sp(2n) is expressed by an integral formula. We have an explicit
formula for the integrand which is a rational 1-form on Sp(2n)
Manifolds Carrying Large Scalar Curvature
Let W = S
E be a complex spinor bundle with vanishing first Chern
class over a simply connected spin manifold M of dimension 5. Up to
connected sums we prove that W admits a twisted Dirac operator with
positive order-0-term in the Weitzenb¨ock decomposition if and only if
the characteristic numbers Aˆ(TM)[M] and ch (E)Aˆ(TM)[M] vanish.
This is achieved by generalizing [2] to twisted Dirac operators
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