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Jan 23, 2020 at 19:29 comment added Saal Hardali It's perhaps not the most important reason but "complex oriented" beyond the existence of chern classes means you can "integrate" cohomology classes along submersions of almost complex manifolds. I believe this was a crucial part in Hirzebruch's original proof of HRR theorem.
Jan 20, 2020 at 13:29 vote accept Andy Jiang
Jan 20, 2020 at 2:07 answer added Eric Peterson timeline score: 26
Jan 16, 2020 at 18:17 answer added user1092847 timeline score: 8
Jan 16, 2020 at 17:43 history asked Andy Jiang CC BY-SA 4.0