Changes between arXiv version 2 and arXiv version 3

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(These are changes in addition to the items in the referee report.)

Many small clarifications of text.  

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

- corrected statement of module to category restrictions

- reduced intermingling for the various n-cat definitions (plain, enriched, A-infinity)

- strengthened n-cat isotopy invariance axiom to allow for homeomorphisms which act trivially elements on the restriction of an n-morphism to the boundary of the ball

- more details on axioms for enriched n-cats

- added details to the construction of traditional 1-categories from disklike 1-categories (Appendix C.1)

- extended the lemmas of Appendix B (about adapting families of homeomorphisms to open covers) to the topological category

- modified families-of-homeomorphisms-action axiom for A-infinity n-categories, and added discussion of alternatives

- added n-cat axiom for existence of splittings, and added similar axiom for fields

- added transversality requirement to product morphism axiom

- added remarks on Morita equivalence for n-categories

- rewrote definition of colimit (in "From Balls to Manifolds" subsection) to allow for more general decompositions; also added more details

- added remark about families of collar maps acting on the blob complex

- small corrections to proof of product theorem (7.1.1)

- added remarks that various homotopy equivalences we construct are well-defined up to a contractible set of choices

- clarified that the surgery cylinder operad action is only up to coherent homotopy

- added some details to the construction of a traditional 2-category from a disk-like 2-category