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Apr 20, 2011 at 8:23 comment added Johannes Ebert Strangely enough, many topologists in Germany tend to call umkehr maps "pushforward". Maybe because otherwise they could be confused with inverse maps; maybe "pushforward" just sounds more faashionable.
Apr 19, 2011 at 18:56 comment added Dmitri Pavlov @Johannes: Usually you use the term Umkehr map when a map going in the other direction is much easier to define, hence the “reversal”.
Apr 19, 2011 at 15:05 comment added Johannes Hahn The term "Umkehrabbildung" (Abbildung being the german word for map) usually refers to and is translated as "inverse map". Do you know why are pushforwards are named like this? I mean $f_\ast$ is usually not invers to $f$ or even to $f^\ast$...
Apr 19, 2011 at 10:21 history answered Dmitri Pavlov CC BY-SA 3.0