How is Abigail's character developed and how/when is she involved in the climax of The Crucible?
The character of Abigail drives much of the action of the play. She acts and others react, including John Proctor. Her assertive and aggressive nature is demonstrated from early on in the play as she discusses what happened in the woods with the other girls and demands that they go along with her story.
Abigail immediately eliminates Mary Warren's idea to confess what they have done and threatens Mary Warren.
We see her Abigail's ability to dominate people. Her ability to manipulate and deceive is shown here as well. In the opening scene, she speaks with Reverend Parris about what happened in the woods, convincingly denying any wrong-doing. With Betty, Tituba and Mary Warren, Abigail reveals the truth of what went on the in woods, acknowledging that she drank blood.
Her ability to deceive and manipulate is repeatedly demonstrated through the play. However, her one honest emotional attachment is also shown early in the play when she speaks with Proctor. She is a person of raw emotion, quick to anger, and able to lie well and quickly. Each of these qualities is demonstrated in the first act.
Abigail is not seen in the second act, but returns in the third and there demonstrates her boldness while further showing her mastery of the art of deception.
This is the closest she comes to the play's climax. She plays a part in Proctor's "climactic" arrest. Putting climactic in quotations is appropriate here because the scene of Proctor's arrest, though tense and full of conflict, is not the play's climax. None of the conflicts of the play are resolved in this moment.
Abigail's involvement here is to continue in her accusations, leading the girls to defeat Mary Warren's attempts at confession and also denying Proctor's true claims about an affair.