Would I be considered an adulterer if I remarried but didn’t give a Gett to my wife? (assuming no unusual circumstances such as a wife who abandoned me)

The question that you ask is a bit tricky to answer as you are trying to have a square peg fit a round hole. The term “adultery” is English and you want to know how it work in Jewish Law. I will try.

In Biblical times men were permitted to have more than one wife. There was a Rabbinic injunction against such a practice about one thousand years ago for Ashkenazic Jews.

One was never permitted to leave a wife in limbo, not living with her husband and not having received a Gett. It is a form of adultery to leave a wife “hanging” and it is considered a form of betrayal and unfaithfulness. Marrying a second wife without releasing the first is not allowed. It would also be deemed living out of wedlock which, although not a form of adultery is nevertheless sinful. For your information, for a Gett in your area you can contact [...].

All the best,
Rabbi Yirmiyahu Benyowitz