If I replaced the fork on my cyclocross bike with a track fork, what would be the effect on the bike geometry? If I replaced the fork on my cyclocross bike, surly cross check, with a track fork, what would be the effect on the bike geometry?  What would be the effect of the modified geometry on bike handling. 

I'm assuming the track fork will be a bit shorter and with less offset than the current fork.  The crosscheck typically has a 400mm long fork with 44mm offset.  I considered swapping it with a surly steamroller fork which has a 375mm axle to crown measurement and 38mm offset Or a Milwalkee bruiser fork, which is the same length 400mm with 32mm offset, which would give me a trail at about 75mm on 32mm tires.
Less fork offset on it's own means more trail. The fork length and wheel size will also affect this though, so you'd need to get all the numbers and maybe draw it out to work out the final difference in trail.

More (longer) trail makes the bike more stable (especially at speed) but less manoeuvrable. Touring and downhill bikes tend to have more trail, while city commuter bikes or sprinting/criterium bikes have less.