Another example concerns the prehomogeneous vector spaces with a cubic relative invariant.
2.
SFT also associates a relative invariant of a Legendrian submanifold of a contact manifold known as relative contact homology.
3.
In other words, in the case that " G " has one-dimensional center, we assume that the semisimple part does " not " act prehomogeneously; it follows that there is a " relative invariant ", i . e ., a function invariant under the semisimple part of " G ", which is homogeneous of a certain degree " d ".
4.
The 3-manifold Floer homologies should also be the targets of relative invariants for four-manifolds with boundary, related by gluing constructions to the invariants of a closed 4-manifold obtained by gluing together bounded 3-manifolds along their boundaries . ( This is closely related to the notion of a topological quantum field theory . ) For Heegaard Floer homology, the 3-manifold homology was defined first, and an invariant for closed 4-manifolds was later defined in terms of it.
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