## 721 Citations

SOME GENERIC DEGREES AND ITS APPLICATION

- 2021

Let A denote the Steenrod algebra at the prime 2 and let k = Z2. An open problem of homotopy theory is to determine a minimal set of A-generators for the polynomial ring Pq = k[x1, . . . , xq] = H(k,…

Structure of the space of $GL_4(\mathbb Z_2)$-coinvariants $\mathbb Z_2\otimes_{GL_4(\mathbb Z_2)} PH_*(\mathbb Z_2^4, \mathbb Z_2)$ in some generic degrees and its application to Singer's cohomological transfer

- Mathematics
- 2021

Let $A$ denote the Steenrod algebra at the prime 2 and let $k = \mathbb Z_2.$ An open problem of homotopy theory is to determine a minimal set of $A$-generators for the polynomial ring $P_q = k[x_1,…

Massey products, toric topology and combinatorics of polytopes

- Mathematics
- 2019

In this paper we introduce a direct family of simple polytopes $P^{0}\subset P^{1}\subset\ldots$ such that for any $k$, $2\leq k\leq n$ there are non-trivial strictly defined Massey products of order…

THE HOPF INVARIANT ONE PROBLEM

- 2019

In this paper we present the Hopf invariant one problem and its solution in terms of complex topological K-theory. Our paper introduces Ktheory starting from the definition of a vector bundle and…

REVIEW ON HIGHER HOMOTOPIES IN THE THEORY OF H-SPACES

- 2017

Higher homotopy in the theory of H-spaces started from the works by Sugawara in the 1950th. In this paper we review the development of the theory of H-spaces associated with it. Mainly there are two…

Local-move-identities for the Z[t,t^{-1}]-Alexander polynomials of 2-links, the alinking number, and high dimensional analogues

- Mathematics
- 2016

A well-known identity (Alex+) - (Alex-)=(t^{1/2}-t^{-1/2}) (Alex0) holds for three 1-links L+, L-, and L0 which satisfy a famous local-move-relation.
We prove a new local-move-identity for the…

Mass Partitions via Equivariant Sections of Stiefel Bundles

- Mathematics
- 2010

We consider a geometric combinatorial problem naturally associated to the geometric topology of certain spherical space forms. Given a collection of $m$ mass distributions on $\mathbb{R}^n$, the…

The Arf-Kervaire Invariant Problem in Algebraic Topology: Introduction

- Mathematics
- 2010

This paper gives the history and background of one of the oldest problems in algebraic topology, along with an outline of our solution to it. A rigorous account can be found in our preprint [HHR].…

## References

SHOWING 1-10 OF 18 REFERENCES

NON-PARALLELIZABILITY OF THE n-SPHERE FOR n > 7.

- Mathematics, MedicineProceedings of the National Academy of Sciences of the United States of America
- 1958

On the parallelizability of the spheres

- Mathematics
- 1958

is always divisible by (2k — 1)!. I wonder if you have noted the connection of this result with classical problems, such as the existence of division algebras, and the parallelizability of spheres.…

On the structure and applications of the steenrod algebra

- Mathematics
- 1958

Nutzungsbedingungen Mit dem Zugriff auf den vorliegenden Inhalt gelten die Nutzungsbedingungen als akzeptiert. Die angebotenen Dokumente stehen für nicht-kommerzielle Zwecke in Lehre, Forschung und…

THE STEENROD ALGEBRA AND ITS DUAL1

- Mathematics
- 1958

1. Summary Let 57 * denote the Steenrod algebra corrresponding to an odd prime p. (See ? 2 for definitions.) Our basic results (? 3) is that 5i* is a Hopf

ON THE COBAR CONSTRUCTION.

- Mathematics, MedicineProceedings of the National Academy of Sciences of the United States of America
- 1956