Editing Thom space (section)

=== Definition of Thom spectrum ===
By definition, the '''Thom spectrum'''<ref>See pp. 8-9 in {{cite arXiv|last=Greenlees|first=J. P. C.|date=2006-09-15|title=Spectra for commutative algebraists|eprint=math/0609452}}</ref> is a sequence of Thom spaces

:<math>MO(n) = T(\gamma^n)</math>

where we wrote <math>\gamma^n\to BO(n)</math> for the [[universal vector bundle]] of rank ''n''. The sequence forms a [[spectrum (topology)|spectrum]].<ref>{{cite web|url=http://math.northwestern.edu/~jnkf/classes/mflds/2cobordism.pdf|title=Math 465, lecture 2: cobordism|first=J.|last=Francis|others=Notes by O. Gwilliam|publisher=Northwestern University}}</ref> A theorem of Thom says that <math>\pi_*(MO)</math> is the unoriented [[cobordism ring]];<ref>{{harvnb|Stong|1968|loc=p. 18}}</ref> the proof of this theorem relies crucially on [[Transversality theorem|Thom’s transversality theorem]].<ref>{{cite web|url=http://math.northwestern.edu/~jnkf/classes/mflds/4transversality.pdf|title=Math 465, lecture 4: transversality|first=J.|last=Francis|others=Notes by I. Bobovka|publisher=Northwestern University}}</ref> The lack of transversality requires that alternative methods be found to compute cobordism rings of, say, [[topological manifold]]s from Thom spectra.