Orientations of $\textit{Spin}$ Bundles and Symplectic Cobordism

Vassily Gorbunov; Nigel Ray

doi:10.2977/prims/1195168855

JournalsprimsVol. 28, No. 1pp. 39–55

Orientations of $Spin$ Bundles and Symplectic Cobordism

Vassily Gorbunov
Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
Nigel Ray
University of Manchester, UK

$Orientations of $\textit{Spin}$ Bundles and Symplectic Cobordism cover$

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Abstract

We analyse certain cofibrations of projective spaces in terms of Thorn complexes of $Spin$ bundles, and by applying the symplectic cobordism functor we are able to deduce new relations amongst the elements $ϕ_{i}$ in the symplectic bordism ring.

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Vassily Gorbunov, Nigel Ray, Orientations of $Spin$ Bundles and Symplectic Cobordism. Publ. Res. Inst. Math. Sci. 28 (1992), no. 1, pp. 39–55

DOI 10.2977/PRIMS/1195168855