All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The Muslim jurists stated that if a woman claims that her husband divorced her and the husband denies it, then it is his statement which is taken into account as he is the one who is sticking to the original status which is that they are married and not divorced. Since you deny that you divorced your wife, then you are still considered as husband and wife as long as your wife does not provide evidence proving her claim. So it is not permissible for her to remarry as she is still your wife. If she marries another man, then their marriage is invalid. Even if we suppose that you divorced her, it is still permissible for you to take her back as long as this divorce is the first or the second one. But if her waiting period expired, (in case you did divorce her) then you cannot take her back except with a new contract and a new dowry. Finally, it should be noted that in such cases, it is more appropriate to refer to an Islamic centre in your country as they are more suitable to study your case in details.
Allaah knows best.