If you need an accessible version of this item please contact JSTOR User Support

On the Kummer Congruences and the Stable Homotopy of BU

Andrew Baker, Francis Clarke, Nigel Ray and Lionel Schwartz
Transactions of the American Mathematical Society
Vol. 316, No. 2 (Dec., 1989), pp. 385-432
DOI: 10.2307/2001355
Stable URL: http://www.jstor.org/stable/2001355
Page Count: 48
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
On the Kummer Congruences and the Stable Homotopy of BU
Preview not available

Abstract

We study the torsion-free part of the stable homotopy groups of the space BU, by considering upper and lower bounds. The upper bound is furnished by the ring PK*(BU) of coaction primitives into which π* S(BU) is mapped by the complex K-theoretic Hurewicz homomorphism π* S(BU) → PK*(BU). We characterize PK*(BU) in terms of symmetric numerical polynomials and describe systematic families of elements by utilizing the classical Kummer congruences among the Bernoulli numbers. For a lower bound we choose the ring of those framed bordism classes which may be represented by singular hypersurfaces in BU. From among these we define families of classes constructed from regular neighborhoods of embeddings of iterated Thom complexes in Euclidean space. Employing techniques of duality theory, we deduce that these two families correspond, except possibly in the lowest dimensions, under the Hurewicz homomorphism, which thus provides a link between the algebra and the geometry. In the course of this work we greatly extend certain e-invariant calculations of J. F. Adams.

Page Thumbnails

  • Thumbnail: Page 
385
    385
  • Thumbnail: Page 
386
    386
  • Thumbnail: Page 
387
    387
  • Thumbnail: Page 
388
    388
  • Thumbnail: Page 
389
    389
  • Thumbnail: Page 
390
    390
  • Thumbnail: Page 
391
    391
  • Thumbnail: Page 
392
    392
  • Thumbnail: Page 
393
    393
  • Thumbnail: Page 
394
    394
  • Thumbnail: Page 
395
    395
  • Thumbnail: Page 
396
    396
  • Thumbnail: Page 
397
    397
  • Thumbnail: Page 
398
    398
  • Thumbnail: Page 
399
    399
  • Thumbnail: Page 
400
    400
  • Thumbnail: Page 
401
    401
  • Thumbnail: Page 
402
    402
  • Thumbnail: Page 
403
    403
  • Thumbnail: Page 
404
    404
  • Thumbnail: Page 
405
    405
  • Thumbnail: Page 
406
    406
  • Thumbnail: Page 
407
    407
  • Thumbnail: Page 
408
    408
  • Thumbnail: Page 
409
    409
  • Thumbnail: Page 
410
    410
  • Thumbnail: Page 
411
    411
  • Thumbnail: Page 
412
    412
  • Thumbnail: Page 
413
    413
  • Thumbnail: Page 
414
    414
  • Thumbnail: Page 
415
    415
  • Thumbnail: Page 
416
    416
  • Thumbnail: Page 
417
    417
  • Thumbnail: Page 
418
    418
  • Thumbnail: Page 
419
    419
  • Thumbnail: Page 
420
    420
  • Thumbnail: Page 
421
    421
  • Thumbnail: Page 
422
    422
  • Thumbnail: Page 
423
    423
  • Thumbnail: Page 
424
    424
  • Thumbnail: Page 
425
    425
  • Thumbnail: Page 
426
    426
  • Thumbnail: Page 
427
    427
  • Thumbnail: Page 
428
    428
  • Thumbnail: Page 
429
    429
  • Thumbnail: Page 
430
    430
  • Thumbnail: Page 
431
    431
  • Thumbnail: Page 
432
    432