Lashi Bandara (UP)
The graphical decomposition for elliptic boundary conditions, obtained by Bär-Ballmann, is an important characterisation of such boundary conditions.
It allows for deformations of these boundary conditions and through its marriage to index theoretic reasoning, yields significant consequences.
In Bär-Bandara, this decomposition is generalised to general first-order operators, beyond the class of operators studied in Bär-Ballmann.
This decomposition demanded dispensing with the use of orthogonality in the original proof, a necessary requirement in the general first-order setting where self-adjointness is lost.
More recently, with Goffeng-Saratchandran, this characterisation has been generalised for general order operators for sufficiently regular boundary conditions.
The aim of this talk is to highlight these decompositions as well as their similarities and differences.
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