Orientations of spin bundles and symplectic cobordism
Vassily Gorbunov,Nigel Ray +1 more
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.read more
Citations
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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.
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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.
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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.
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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.
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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
Pierre E. Conner,E. E. Floyd +1 more
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.