The Relation of Cobordism to K-theoriesSpringer-Verlag, 1966 - 110 pages |
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Page 1
... Thom space of ; we call J ( 3 ) the Thom class of § . Similarly given an SU ( 4k ) -bundle there is constructed a Thom class t ( 5 ) ɛ KO ( M ( 5 ) ) ; and given an SU ( 4k + 2 ) -bundle there is constructed a class s ( 5 ) & KSp ( M ...
... Thom space of ; we call J ( 3 ) the Thom class of § . Similarly given an SU ( 4k ) -bundle there is constructed a Thom class t ( 5 ) ɛ KO ( M ( 5 ) ) ; and given an SU ( 4k + 2 ) -bundle there is constructed a class s ( 5 ) & KSp ( M ...
Page 19
... Thom space M ( ) is canonically isomorphic to E ( ) Sp ( 1 ) / Sp ( 1 ) . Proof . Recall that D ( ) = 4 4 E ( ) × D / Sp ( 1 ) , where D is the unit disk in the space H of quaternions . ( ( e , v ) ) . 4 Points of D ( 5 ) are denoted by ...
... Thom space M ( ) is canonically isomorphic to E ( ) Sp ( 1 ) / Sp ( 1 ) . Proof . Recall that D ( ) = 4 4 E ( ) × D / Sp ( 1 ) , where D is the unit disk in the space H of quaternions . ( ( e , v ) ) . 4 Points of D ( 5 ) are denoted by ...
Page 49
... Thom space M ( ) is identified with HP ( n + 1 ) . Letting n n → ∞ , we obtain a universal Sp ( 1 ) -bundle over HP ( ∞ ) , and = MSp ( 1 ) M ( 5 ) ≈ HP ( ∞ ) . For each n , the inclusion i : HP ( n ) C HP ( ) represents an element ...
... Thom space M ( ) is identified with HP ( n + 1 ) . Letting n n → ∞ , we obtain a universal Sp ( 1 ) -bundle over HP ( ∞ ) , and = MSp ( 1 ) M ( 5 ) ≈ HP ( ∞ ) . For each n , the inclusion i : HP ( n ) C HP ( ) represents an element ...
Contents
The Thom Isomorphism in Ktheory | 1 |
Cobordism Characteristic Classes | 38 |
UManifolds with Framed Boundaries | 69 |
Copyright | |
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abelian group algebra base point bordism bordism classes bordism groups bundle map ch+k characteristic classes Chern classes Chern numbers closed U-manifold cobordism cohomology theory complex inner product complex vector space composition consider COROLLARY CP(n CW pair X,A define denote diagram dimension Dold epimorphism fiber finite CW complex finite CW pair fr)-manifold framed manifold Hence homotopy class Hopf HP(n identified induced inner product space integer K-theory kernel KSP(X LEMMA line bundle linear M²n map f Milnor monomial MSU 4k MU(k multiplicative cohomology theory n)-bundle ñ¹ ñ¹(x P₁ partition polynomial Proof quaternionic quaternionic vector space Similarly stable tangent bundle stably framed manifold SU(n Suppose theorem Thom class Thom space Todd genus trivial U-structure U(n)-bundle vector space bundle Z-graded εΩ Ωυ