Like?:
An abnormal subgroup
Connected/Path-connected/Compact/Metrizable locally but not globally
An irregular space (It's okay to call a polyhedron irregular, but what about a space?)
An abnormal space
An incompletely regular/normal/metrizable space
An imperfectly normal space
Complicatedly connected
I'd say some of these are okay. The preferred way to negate mathematical adjectives seems to be to add the prefix "non-" even when English antonyms exist. Thus,
Your use of the word "global" in the context of connectedness or compactness would seem redundant. "Incompletely" and "Imperfectly" seem a little too clever. "Complicatedly" is a mouthful, and if it's supposed to mean the negation of "simply connected" then there's already a term for that: "multiply connected". (The pairs "simple/multiple" and "ordinary/singular" are common.)
In general, you want your writing to be understood. Use the existing language if available, or have a good reason to reject it, and always define your terms. Non-native speakers of English (or whatever discourse language you're writing in) may not be as familiar with the more uncommon modes of negation or pairs of antonyms.