@-_Ashley-B-Potter_- The responses above have good information, and here is some more background /overview.
The parcel fabric uses the standard geodatabase topology. That topology gets created for you when you create a new parcel fabric, and there are geodatabase topology rules set up for you between the line feature class and polygon feature class for each of the parcel types you create.
The standard editing tools and map topology will all work with the parcel fabric features. While there are also additional tools that work with the fabric, you are free to use any and all standard editing tools and GP tools with the parcel fabric features and parcel feature layers.
Whether or not there is a topology rule does not really matter for your specific scenario, but as Jason mentions, you do need to specify either Map topology or the fabric's gdb topology in the edit tab, to enable topological editing.
Based on your description it sounds like the editing tools to explore/research for your scenario are:
Edit a toplogical vertex
Move a topology node
-Tim