On Lerman’s Cut Construction

On the way through literature the author stumbled across Lerman’s paper Contact cuts [Ler01], originally just to understand the broader context in some other work. However, besides the motivation of merely comprehending the general concept, he realized that the proofs presented by Lerman are quite tricky and leave out many necessary information. Thus, the idea arose to ‘round off’ Lerman’s arguments in [Ler01] and check his proofs in detail. As a consequence, many but not all of his theorems can be found in this thesis, sometimes slightly modified or even corrected. Unfortunately, this also means that there is a motley assortment of propositions, not all of them are interconnected in a way the au- thour wished for in the first place, especially since there will be no final application of the cut construction: This was initially not intended and, additionally, the author simply lacks the knowledge in contact geometry to understand the last section in Contact cuts. Instead, the style below will be considerably technical with little to no examples or motivation and it is strongly recommended to at least take a look at Lerman’s paper while reading the the- sis. Nonetheless, the author hopes to still make a small contribution by reviewing Lerman’s cut construction and correcting details if necessary, and at best help the reader to better understand the subject matter of Contact cuts.