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Problems in the Steenrod algebra
 Bull. London Math. Soc
, 1998
"... This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development ..."
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Cited by 30 (1 self)
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This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of the Steenrod algebra and its connections to the various topics indicated below. Contents 1 Historical background 4
A unified formula for Steenrod operations in flag manifolds
, 2005
"... A unified formula for Steenrod operations in flag manifolds ..."
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Cited by 9 (3 self)
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A unified formula for Steenrod operations in flag manifolds
The Combinatorics Of Steenrod Operations On The Cohomology Of Grassmannians
 Adv. Math
, 1997
"... The study of the action of the Steenrod algebra on the mod p cohomology of spaces has many applications to the topological structure of those spaces. In this paper we present combinatorial formulas for the action of Steenrod operations on the cohomology of Grassmannians, both in the Borel and the ..."
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Cited by 5 (1 self)
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The study of the action of the Steenrod algebra on the mod p cohomology of spaces has many applications to the topological structure of those spaces. In this paper we present combinatorial formulas for the action of Steenrod operations on the cohomology of Grassmannians, both in the Borel and the Schubert picture. We consider integral lifts of Steenrod operations, which lie in a certain Hopf algebra of differential operators. The latter has been considered recently as a realization of the LandweberNovikov algebra in complex cobordism theory; it also has connections with the action of the Virasoro algebra on the boson Fock space. Our formulas for Steenrod operations are based on combinatorial methods which have not been used before in this area, namely Hammond operators and the combinatorics of Schur functions. We also discuss several applications of our formulas to the geometry of Grassmannians.
Steenrod structures on categorified quantum groups, available at arXiv:math.QA/1304.7152
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Copyright and moral rights for this thesis are retained by the author
, 2006
"... A copy can be downloaded for personal noncommercial research or study, without prior permission or charge This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the Author The content must not be changed in any way or sold commercially in any ..."
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A copy can be downloaded for personal noncommercial research or study, without prior permission or charge This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the Author The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the Author When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given
Contents
"... This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may nd of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of ..."
Abstract
 Add to MetaCart
This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may nd of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of the Steenrod algebra and its connections to the various topics indicated below.
Steenrod operations on Schubert classes
, 2003
"... Let G be a compact connected Lie group and H the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan numbers of G. ..."
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Let G be a compact connected Lie group and H the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan numbers of G.