ON <i>SU</i> × <i>SU</i>-BORDISM

Ray, Nigel; Switzer, Robert M.

doi:10.1093/qmath/21.2.137

Cited by 5 publications

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“…(ii) El i6 = Z a o n a^a n d^e = # § >6 ®#*(MSU). (iii) d% 5 , using (5-1) and (5)(6)(7)(8)(9)(10)(11)(12)(13)(14). Note that we cannot say how d% 4 works until we know whether a(2x 1 ) = <$> x or 0.…”

Section: K >mentioning

confidence: 99%

“…(2x 1 )) = a.msu(2a; 1 ) = 0 since a has order 2 and <x.s 2 eMSU 5 = 0. Hence by(5)(6)(7)(8)(9)(10)(11)(12), a(2x x ) =j = <j> 1 in MSp 5 , so a(2a; 1 ) = 0. (5-17) Construction.…”

mentioning

confidence: 99%

“…E\ 8 Aas generators x\ and 2x 2 (see footnote to (3-6)).Proof. The proof of(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) shows that the extension problem is split, so by (2-2) E% 8 ^ MSp 8 must be generated by x\ and 2a; 2 -These are (3-1) and (3-2) of (8).Note in (5-25) the indecomposable elements of Tors MSp*, viz. <j> x e MSp s , <j> 2 e MSp 13 and Tj^eMSpw, and the non-trivial relations in the higher torsion dimensions 13, 14, 17 and 18.…”

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confidence: 99%

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The symplectic bordism ring

Ray

1972

Math. Proc. Camb. Phil. Soc.

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This paper is concerned with the symplectic bordism ring MSp*, whose structure is still largely unknown despite the partial results of Liulevicius(3), Novikov(4) and Stong(lO). It is the first of two elaborating(8), and it relies completely on (7) for notation and prerequisites. In particular we assume the reader to be familiar with (7), section 8, which establishes the relation between the Sp Hattori-Stong conjecture (that KO decides MSp) and the spectral sequenceWe are here concerned entirely with computations in this spectral sequence.

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Section: K >mentioning

confidence: 99%

“…(2x 1 )) = a.msu(2a; 1 ) = 0 since a has order 2 and <x.s 2 eMSU 5 = 0. Hence by(5)(6)(7)(8)(9)(10)(11)(12), a(2x x ) =j = <j> 1 in MSp 5 , so a(2a; 1 ) = 0. (5-17) Construction.…”

mentioning

confidence: 99%

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confidence: 99%

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The symplectic bordism ring

Ray

1972

Math. Proc. Camb. Phil. Soc.

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“…We say g is pure if and only if it is a monomorphism onto a pure subgroup of G 2 -Note that if G 2 is torsion free, the concept of g being pure coincides exactly with that of preserving integrality as defined in similar situations elsewhere (e.g. in (15)).…”

Section: N I G E L R a Ymentioning

confidence: 99%

Some results in generalized homology, K-theory and bordism

Ray

1972

Math. Proc. Camb. Phil. Soc.

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This paper is designed to pave the way for the author's work on the symplectic bordism ring MSp*(12), (13). We here discuss all the notation used, and collect together all the theorems quoted therein. At the same time, I hope that some of the results presented here might be of interest in their own right. Our central theme is the study of the hurewicz map e: S*(X) → E*(X), both in general and certain specific cases.

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“…We work in the context of double complex cobordism, whose properties we have developed in a preliminary article [8]. So far as we are aware, double cobordism theories first appeared in [20], and in the associated work [23]. To emphasize our geometric intent we return to the notation of the 60s, and write bordism and cobordism functors as Ω * ( ) and Ω * ( ) throughout.…”

Section: Introductionmentioning

confidence: 99%

Flag manifolds and the Landweber–Novikov algebra

Buchstaber¹,

Ray²

1998

Geom. Topol.

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We investigate geometrical interpretations of various structure maps associated with the Landweber-Novikov algebra S * and its integral dual S * . In particular, we study the coproduct and antipode in S * , together with the left and right actions of S * on S * which underly the construction of the quantum (or Drinfeld) double D(S * ). We set our realizations in the context of double complex cobordism, utilizing certain manifolds of bounded flags which generalize complex projective space and may be canonically expressed as toric varieties. We discuss their cell structure by analogy with the classical Schubert decomposition, and detail the implications for Poincaré duality with respect to double cobordism theory; these lead directly to our main results for the Landweber-Novikov algebra. and its subalgebra G * , together with the canonical isomorphism which identifies them with the Hopf algebroid A U * and its sub-Hopf algebra S * respectively. In section 3 we study the geometry and topology of the bounded flag manifolds B(Z n+1 ),

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ON SU × SU-BORDISM

Cited by 5 publications

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The symplectic bordism ring

The symplectic bordism ring

Some results in generalized homology, K-theory and bordism

Flag manifolds and the Landweber–Novikov algebra

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