Massey products in K-theory

1970 ◽  
Vol 68 (2) ◽  
pp. 303-320 ◽  
Author(s):  
V. P. Snaith
Keyword(s):  
Vector Bundles ◽  
Higher Order ◽  
Massey Products ◽  
Cohomology Operations ◽  
K Theory

The aim of this paper is to reformulate the work of Massey(6), and Spanier(9, 10), on higher order cohomology operations, in terms of vector bundles in such a way as to produce geometrically some higher order operations in K-theory, which we will call Massey products.

Massey products in K-theory. II

1971 ◽  
Vol 69 (2) ◽  
pp. 259-289 ◽  
Author(s):  
V. P. Snaith
Keyword(s):  
Spectral Sequence ◽  
Higher Order ◽  
Massey Products ◽  
K Theory ◽  
Image Position

0. Introduction: In (14), higher order operations in K-theory, called Massey products, were introduced. These were motivated by the construction, in (7), of a spectral sequence in equivariant K-theory

scholarly journals On q-th Derivative of Vector Bundles

1967 ◽  
Vol 29 ◽  
pp. 121-126
Author(s):  
Akikuni Kato
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Present Note ◽  
Higher Order ◽  
Enumerative Geometry ◽  
Sheaf Theory ◽  
Definition Of

In the present note we shall be concerned with the improvement of fundamental definitions in higher order enumerative geometry which has been recently given by W. F. Pohl. Pohl’s definition of q-th derivative of vector bundle is very complicated. We shall give a simpler and more reasonable definition of the q-th derivative of vector bundle in terms of sheaf theory and simplify the proofs in [P]. We shall also give a definition of higher order singularity of map.

scholarly journals The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra

2019 ◽  
Vol 30 (11) ◽  
pp. 1950057 ◽  
Author(s):  
M. Izumi ◽  
T. Sogabe
Keyword(s):  
Automorphism Group ◽  
Vector Bundles ◽  
Group Structure ◽  
Cuntz Algebra ◽  
Classifying Space ◽  
Cuntz Algebras ◽  
K Theory ◽  
Continuous Fields

We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra [Formula: see text] for finite [Formula: see text] in terms of K-theory. We show that there is an example of a space for which the homotopy set is a noncommutative group, and hence, the classifying space of the automorphism group of the Cuntz algebra for finite [Formula: see text] is not an H-space. We also make an improvement of Dadarlat’s classification of continuous fields of the Cuntz algebras in terms of vector bundles.

K-Theory of Vector Bundles, of Modules, and of Idempotents

2007 ◽  
pp. 45-54
Author(s):  
D. Husemöller ◽  
M. Joachim ◽  
B. Jurčo ◽  
M. Schottenloher
Keyword(s):  
Vector Bundles ◽  
K Theory

On the differentials in the Adams spectral sequence

1964 ◽  
Vol 60 (3) ◽  
pp. 409-420 ◽  
Author(s):  
C. R. F. Maunder
Keyword(s):  
Spectral Sequence ◽  
Higher Order ◽  
Adams Spectral Sequence ◽  
Steenrod Algebra ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Cohomology Operations ◽  
Image Position

In this paper, we shall prove a result which identifies the differentials in the Adams spectral sequence (see (1,2)) with certain cohomology operations of higher kinds, in the sense of (4). This theorem will be stated precisely at the end of section 2, after a summary of the necessary information about the Adams spectral sequence and higher-order cohomology operations; the proof will follow in section 3. Finally, in section 4, we shall consider, by way of example, the Adams spectral sequence for the stable homotopy groups of spheres: we show how our theorem gives a proof of Liulevicius's result that , where the elements hn (n ≥ 0) are base elements ofcorresponding to the elements Sq2n in A, the mod 2 Steenrod algebra.

scholarly journals Central Cohomology Operations and K-Theory

2014 ◽  
Vol 57 (3) ◽  
pp. 699-711
Author(s):  
Imma Gálvez-Carrillo ◽  
Sarah Whitehouse
Keyword(s):  
Complex Cobordism ◽  
Cohomology Operations ◽  
K Theory ◽  
Stable Degree

AbstractFor stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP〈n⌰ for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory.

scholarly journals Equivariant KK-theory for generalised actions and Thom isomorphism in groupoid twisted K-theory

2013 ◽  
Vol 13 (1) ◽  
pp. 83-113 ◽  
Author(s):  
El-Kaïoum M. Moutuou
Keyword(s):  
Vector Bundles ◽  
Isomorphism Theorem ◽  
Locally Compact ◽  
Bott Periodicity ◽  
C Algebras ◽  
Thom Isomorphism ◽  
K Theory ◽  
Thom Isomorphism Theorem

AbstractWe develop equivariant KK–theory for locally compact groupoid actions by Morita equivalences on real and complex graded C*-algebras. Functoriality with respect to generalised morphisms and Bott periodicity are discussed. We introduce Stiefel-Whitney classes for real or complex equivariant vector bundles over locally compact groupoids to establish the Thom isomorphism theorem in twisted groupoid K–theory.

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