We show that the Kervaire invariant one elements θ_jϵπ_2^j+1-2S^0 exist only for j≤ 6. By
Browder's Theorem, this means that smooth framed manifolds of Kervaire invariant one exist …

We present a detailed analysis of 2-complete stable homotopy groups, both in the classical
context and in the motivic context over $\mathbb {C} $. We use the motivic May spectral …

The connective topological modular forms spectrum, $ tmf $, is in a sense initial among
elliptic spectra, and as such is an important link between the homotopy groups of spheres …

This book is a compilation of lecture notes that were prepared for the graduate
course``Adams Spectral Sequences and Stable Homotopy Theory''given at The Fields …

Exploring the full scope of differential topology, this comprehensive account of geometric
techniques for studying the topology of smooth manifolds offers a wide perspective on the …

[en] This manuscript contains extended notes of the lectures presented by the author at the
summer school'High-dimensional Manifold Theory'in Trieste in May/June 2001. It is written …

arXiv:2001.04511v2 [math.AT] 17 Jun 2020 Page 1 arXiv:2001.04511v2 [math.AT] 17 Jun 2020
More stable stems Daniel C. Isaksen Guozhen Wang Zhouli Xu Author address: Department of …

We discuss the current state of knowledge of stable homotopy groups of spheres. We
describe a computational method using motivic homotopy theory, viewed as a deformation …

We prove that the 2-primary 61 is zero. As a consequence, the Kervaire invariant element
\theta_5 is contained in the strictly defined 4-fold Toda bracket (2,\theta_4\theta_4,2) …

This textbook is an introduction to the modern foundations of stable homotopy theory and
'algebra'over structured ring spectra, based on symmetric spectra. We begin with a quick …