Show that if the homology of a spectrum is free, then its Atiyah-Hirzebruch spectral sequence for any (co)homology theory with torsion-free coefficients degenerates at E_2.
No, it really is little. Like, given the appropriate prerequisites (which pretty much any second-year grad student in algebraic topology should have), it's not a superhard or scary problem at all.
Hehe, I actually really enjoy your FLMPotD posts. My take: I look up every word in them that I don't know and try to understand what each object is.
In this post: * homology * spectrum * spectral sequence * Atiyah-Hirzebrauch spectral sequence * cohomology theory * homology theory * torsion-free * degenerates * E_2
Aka, I recognized the words: show, that, if, the, of, a, then, its, for, any, with, coefficients, at. And homology, cohomology, and spectral sequence are vaguely in the limit of my vocabulary at this point.
Maybe I'm weird, but I like regularly being confronted with the enormity of what I don't know and may or may not ever figure out. :)
Well, in this context "coefficients" doesn't have a meaning in itself, rather "coefficients of a (co)homology theory" has a specific meaning. Also, for what it's worth it's basically impossible to know what "spectral sequence" means without also knowing "degenerates" and "E_2".
Comments 6
Reply
Reply
Reply
Reply
In this post:
* homology
* spectrum
* spectral sequence
* Atiyah-Hirzebrauch spectral sequence
* cohomology theory
* homology theory
* torsion-free
* degenerates
* E_2
Aka, I recognized the words: show, that, if, the, of, a, then, its, for, any, with, coefficients, at. And homology, cohomology, and spectral sequence are vaguely in the limit of my vocabulary at this point.
Maybe I'm weird, but I like regularly being confronted with the enormity of what I don't know and may or may not ever figure out. :)
Reply
Reply
Leave a comment