Complex sentence: Rosecrans's initial movements on June 23 took Bragg by surprise--while keeping Polk's corps occupied with small actions in the center of the Confederate line, Rosecrans sent the majority of his army around Bragg's right flank.
Split into simpler sentences: Rosecrans's initial movements on June 23 took Bragg by surprise. While keeping Polk's corps occupied with small actions in the center of the Confederate line, Rosecrans sent the majority of his army around Bragg's right flank.