Your line
Eigen::VectorXi c = Eigen::VectorXi::Map(a.data(), a.size());
doesn't "directly map a std::vector<unsigned> to an Eigen::VectorXi," rather, it copies the data to a new Eigen::VectorXi. If you want to wrap the existing data array with Eigen functionality, you should use something like:
Eigen::Map<Eigen::VectorXi> wrappedData(a.data(), a.size());
You can then use use wrappedData as you would any other VectorXi with the exception of resizing the underlying data (that's still owned by the std::vector). See the documentation for more details.
If you're trying to avoid copying the data to a std::vector<int> then you can use a "custom" matrix type, i.e.
typedef Eigen::Matrix<unsigned int, Eigen::Dynamic, 1> VectorXui;
Eigen::Map<VectorXui> wrappedData(a.data(), a.size());