Generators of the unoriented bordism ring which are fibered over products of projective spacesRP(2 r −1)

1996 ◽  
Vol 91 (1) ◽  
pp. 235-245 ◽  
Author(s):  
Oswald Gschnitzer
Keyword(s):  
Bordism Ring

scholarly journals On a construction in bordism theory

1986 ◽  
Vol 29 (3) ◽  
pp. 413-422 ◽  
Author(s):  
Nigel Ray
Keyword(s):  
Line Bundles ◽  
Complex Line ◽  
Surgery Theory ◽  
Normal Bundles ◽  
Bordism Ring ◽  
Complex Line Bundles

In [2], R. Arthan and S. Bullett pose the problem of representing generators of the complex bordism ring MU* by manifolds which are totally normally split; i.e. whose stable normal bundles are split into a sum of complex line bundles. This has recently been solved by Ochanine and Schwartz [8] who use a mixture of J-theory and surgery theory to establish several results, including the following.

Realizing symplectic bordism classes

1972 ◽  
Vol 71 (2) ◽  
pp. 301-305 ◽  
Author(s):  
Nigel Ray
Keyword(s):  
Low Dimensions ◽  
Bordism Ring

This is the second of two papers elaborating (4), and is concerned with the more geometrical aspects of the symplectic bordism ring in low dimensions. As such, it is a natural sequel to (2). However, the reader who does not care for the algebra therein need only consult (3), in which appears all the notation and prerequisites for this paper.

A Note on the Symplectic Bordism Ring

1971 ◽  
Vol 3 (2) ◽  
pp. 159-162 ◽  
Author(s):  
Nigel Ray
Keyword(s):  
Bordism Ring

Addendum to a paper of Conner and Floyd

1966 ◽  
Vol 62 (2) ◽  
pp. 171-175 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Multiplicative Structure ◽  
Additive Structure ◽  
Bordism Ring

In two recent papers of Conner and Floyd ((2)) and ((3)), the additive structure of the SU-cobordism (or bordism) ring was completely determined. The object of this note is to point out that their results can also be used to determine the somewhat complicated multiplicative structure.

Some results in generalized homology, K-theory and bordism

1972 ◽  
Vol 71 (2) ◽  
pp. 283-300 ◽  
Author(s):  
Nigel Ray
Keyword(s):  
Central Theme ◽  
Bordism Ring ◽  
K Theory ◽  
The Way

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.

scholarly journals Stiefel–Whitney numbers for singular varieties

2011 ◽  
Vol 150 (2) ◽  
pp. 273-289
Author(s):  
CARL McTAGUE
Keyword(s):  
Vector Space ◽  
Upper Bound ◽  
Elliptic Genus ◽  
Singular Varieties ◽  
Whitney Numbers ◽  
Bordism Ring ◽  
Genus One ◽  
Gorenstein Variety

AbstractThis paper determines which Stiefel–Whitney numbers can be defined for singular varieties compatibly with small resolutions. First an upper bound is found by identifying theF2-vector space of Stiefel–Whitney numbers invariant under classical flops, equivalently by computing the quotient of the unoriented bordism ring by the total spaces ofRP3bundles. These Stiefel–Whitney numbers are then defined for any real projective normal Gorenstein variety and shown to be compatible with small resolutions whenever they exist. In light of Totaro's result [Tot00] equating the complex elliptic genus with complex bordism modulo flops, equivalently complex bordism modulo the total spaces of3bundles, these findings can be seen as hinting at a new elliptic genus, one for unoriented manifolds.

The symplectic bordism ring

1972 ◽  
Vol 71 (2) ◽  
pp. 271-282 ◽  
Author(s):  
Nigel Ray
Keyword(s):  
Spectral Sequence ◽  
Section 8 ◽  
Bordism Ring ◽  
Image Position

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.

scholarly journals On the bordism ring of complex projective space

1973 ◽  
Vol 37 (1) ◽  
pp. 267-270 ◽  
Author(s):  
Claude Schochet
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Bordism Ring ◽  
Complex Projective

scholarly journals Nilpotence in the symplectic bordism ring

2017 ◽  
pp. 161-165
Author(s):  
Justin Noel
Keyword(s):  
Bordism Ring
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