Changes between arXiv version 2 and arXiv version 3
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Many small clarifications of text.  

Also many typos corrected.


The most significant changes are:

- added to acknowledgements
- clarified definition of splittable
- changed to pitchfork notation for splittable subsets of fields
- added definition of collaring homeomorphism
- improved definition of bordism n-category
- fixed definition of a refinement of a ball decomposition (intermediate manifolds should also be disjoint unions of balls)
- added brief definition of monoidal n-categories
- fixed statement of compatibility of product morphisms with gluing
- added remark about manifolds which do not admit ball decompositions; restricted product theorem (7.1.1) to apply only to these manifolds
- added remarks about categories of defects
- clarified that the "cell complexes" in string diagrams are actually a bit more general
- added remark to insure that the poset of decompositions is a small category
- rewrote definition of colimit (in "From Balls to Manifolds" subsection) to allow for more general decompositions; also added more details
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