I've come to like linear algebra far more than analysis and was wondering how much analysis one would be required to learn in order to pursue a career in research in an algebraic field. For example, at the graduate level, if I were interested in focusing on algebraic topology or algebraic geometry then would learning the contents of analysis 2, real analysis, and differential equations be enough before one exclusively focuses on algebra core subjects? Is it common for mathematicians of one field to be very weak in other fields? Like somebody who does exceptional research in algebraic geometry who would struggle with solving problems in a complex analysis text?
Thanks in advance!