For references of embedded Morse theory, or so-called relative morse theory of a pair, I have found R.W. Sharpe's "Total Absolute Curvature and Embedded Morse numbers" totally not helpful. For further details, Sharpe refers the reader to B. Perron's "Pseudo-Isotopies de plongements en codimension 2", another reference which for me is totally opaque.

When learning morse theory for the first time, there is the standard example of the height function on the torus in 3-space--and this an example which one 'sees' and bears in mind throughout. However I find myself without any such 'basic' example for the relative morse theory. Even the instance of considering how the height function would yield a handlebody decomposition of the complement of the torus in 3-space is something that I don't 'see'.

Can anybody refer me to some basic examples of the embedded morse theory, or to some further literature?