scispace - formally typeset
Open AccessJournal ArticleDOI

Orientations of spin bundles and symplectic cobordism

TLDR
In this article, the authors analyse certain cofibrations of projective spaces in terms of Thorn complexes of Spin bundles, and by applying the symplectic cobordism functor they are able to deduce new relations amongst the elements 0t in the bordism ring.
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 0t in the symplectic bordism ring.

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Citations
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Journal ArticleDOI

The transfer and symplectic cobordism

TL;DR: In this article, the transfer homomorphism for projective bundles associated with universal Spin(m) bundles, m = 3, 4, 5, has been investigated and the main result is the nilpotency fomula φi = 0, ∀i ≥ 1 for N.
Journal ArticleDOI

Singularities and higher torsion in symplectic cobordism

TL;DR: In this article, the Adams-Novikov spectral sequence was used to construct higher two-torsion elements of all orders in the symplectic cobordism ring with singularities.
Journal ArticleDOI

Adams spectral sequence and higher torsion in MSp

TL;DR: In this article, the Adams spectral sequence was used to determine an upper bound for the order of these elements of higher torsion in the symplectic cobordism ring, which is the same as in this paper.
Journal ArticleDOI

On the Buchstaber Subring in MSp

TL;DR: In this article, a formula was given to calculate the last n number of characteristic classes of the tensor product of Spin(3)- and Sp(n)-bundles through its Þrst 2n number of character-istic classes and through characteristic classes.
Journal ArticleDOI

Characteristic classes and transfer relations in cobordism

TL;DR: In this article, it was shown that most of the 4n-dimensional generators, for n small, after multiplication by the Ray elements Φ i, i ≥ 0, land in the ideal generated by Ray elements of low dimension.
References
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Book

Complex Cobordism and Stable Homotopy Groups of Spheres

TL;DR: An introduction to the homotopy groups of spheres is given in this article, where the Adams spectral sequence and the Adams-Novikov spectral sequence are used to construct the spectral groups.
Book

Lectures on Lie groups

TL;DR: In this article, the authors present a basic text for compact Lie groups, "Lectures in Lie Groups", which should be a useful reference for any mathematician who would like to learn the basic results for compact lie groups.
Journal ArticleDOI

The transfer map and fiber bundles

TL;DR: In this article, it was shown that there exists a transfer associated with the fiber bundle p: E + B. The main purpose of this paper is to construct an Smap T: B+ + E+ which induces the homomorphism Q (+ denoting disjoint union with a base point).
Book

The relation of cobordism to k-theories

TL;DR: In this paper, the Pontrjagin-Thom construction of bordism is given in detail, and the ring structure of Ω ∗ is discussed. But it is not discussed in detail in this paper.