What was the name of the battle that resulted from lee’s invasion of the north

I'm not sure I understand the question very well, but the end of the Battle of Antietam (or Sharpsburg) resulted in Lee's first invasion of the North.

the most famous of all the units fighting in cuba, the "rough riders" was the name given to the first u.s. volunteer cavalry under the leadership of theodore roosevelt. roosevelt resigned his position as assistant secretary of the navy in may 1898 to join the volunteer cavalry. the original plan for this unit called for filling it with men from the indian territory, new mexico, arizona, and oklahoma. however, once roosevelt joined the group, it quickly became the place for a mix of troops ranging from ivy league athletes to glee-club singers to texas rangers and indians.