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Template:Orphan In algebraic topology, a complex-orientable cohomology theory is a multiplicative cohomology theory E such that the restriction map is surjective. An element of that restricts to the canonical generator of the reduced theory is called a complex orientation. The notion is central to Quillen's work relating cohomology to formal group laws.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.
If , then E is complex-orientable.
Examples:
- An ordinary cohomology with any coefficient ring R is complex orientable, as .
- A complex K-theory, denoted by K, is complex-orientable, as (Bott periodicity theorem)
- Complex cobordism, whose spectrum is denoted by MU, is complex-orientable.
A complex orientation, call it t, gives rise to a formal group law as follows: let m be the multiplication
where denotes a line passing through x in the underlying vector space of . Viewing
let be the pullback of t along m. It lives in
and one can show it is a formal group law (e.g., satisfies associativity).