Changing research topics completely when entering graduate school? In my undergraduate years I mainly focused on analysis, and have done two research projects in analysis. 
However, when the application results turned out, the best school that gave me an offer is not particularly strong in analysis, but in topology/ geometry. This is something I am also interested in but have no true working experience.
Thus I wonder whether it is common for a graduate school to work in a totally new area? If it is common I would accept that offer, otherwise I will go to a less well-known school but a little bit stronger in analysis.
Thanks very much!

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*I think this question should migrated to Academia SE. Math SE users who are most able and willing to give career advice tend to also be users of Academia. 

*Yes, it is very common for graduate-level research to be in an area that is completely different from the area of undergraduate research. It is also common to excel in graduate-level research, and in mathematical career afterwards, without having done any undergraduate research at all. 

*Localizing to the U.S. academic market and to the current period of time: the probability of landing a postdoctoral position will be greater if you write a dissertation in Geometry/Topology at a more prestigious department than if you write a dissertation in Analysis at a less prestigious department. (Of course, it greatly depends on what's in the thesis. But the field matters too.)
