Add to ORKGWe bound the volume of the homotopy groups of the 2-local Goodwillie approximations of a sphere in terms of the amount of $2$-torsion in the stable stems, providing a Goodwillie-theoretic refinement of a result of Burklund and Senger (arXiv:2203.00670). At the $2^k$-excisive approximation, this bound is obtained by `multiplying the stable answer by a polynomial of degree $k$'. The main tool is Behrens' Goodwillie-EHP Long Exact Sequence.Comment: Substantial revision after the release of Burklund and Senger's preprint, which changed the landscape dramatically. 11 pages, comments welcome
Cataloged from PDF version of article.A classical conjecture in transformation group theory states t...
We construct certain unstable higher-order homotopy operations indexed by the simplex categories of ...
Here the existence of a new homomorphism $P_{\omega} : \Theta_{\mathbb{Z}}^3 \to \mathbb{Z}$ is prov...
We study the infinite generation in the homotopy groups of the group of diffeomorphisms of $S^1 \tim...
We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a new co...
We show that the homology torsion growth of a free-by-cyclic group with polynomially growing monodro...
We determine $\pi_*(BDiff_\partial(D^{2n})) \otimes \mathbb{Q}$ for $2n \geq 6$ completely in degree...
The $2$-primary homotopy $\beta$-family, defined as the collection of Mahowald invariants of Mahowal...
This thesis studies the limiting behaviour of the torsion in the homotopy groups πn(X) of a space X ...
We develop a higher semiadditive version of Grothendieck-Witt theory. We then apply the theory in th...
We prove new vanishing results on the growth of higher torsion homologies for suitable arithmetic la...
We analyze the homological behavior of the attaching maps in the 2–local Goodwillie tower of the id...
In this paper, we propose a new method to the homotopy classification of maps between $(n-1)$-connec...
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Abstract: We construct a zig–zag from the once delooped space of pseudoisotopies of a closed 2n-disc...
Cataloged from PDF version of article.A classical conjecture in transformation group theory states t...
We construct certain unstable higher-order homotopy operations indexed by the simplex categories of ...
Here the existence of a new homomorphism $P_{\omega} : \Theta_{\mathbb{Z}}^3 \to \mathbb{Z}$ is prov...
We study the infinite generation in the homotopy groups of the group of diffeomorphisms of $S^1 \tim...
We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a new co...
We show that the homology torsion growth of a free-by-cyclic group with polynomially growing monodro...
We determine $\pi_*(BDiff_\partial(D^{2n})) \otimes \mathbb{Q}$ for $2n \geq 6$ completely in degree...
The $2$-primary homotopy $\beta$-family, defined as the collection of Mahowald invariants of Mahowal...
This thesis studies the limiting behaviour of the torsion in the homotopy groups πn(X) of a space X ...
We develop a higher semiadditive version of Grothendieck-Witt theory. We then apply the theory in th...
We prove new vanishing results on the growth of higher torsion homologies for suitable arithmetic la...
We analyze the homological behavior of the attaching maps in the 2–local Goodwillie tower of the id...
In this paper, we propose a new method to the homotopy classification of maps between $(n-1)$-connec...
We prove that the quotient of the integer homology cobordism group by the subgroup generated by the ...
Abstract: We construct a zig–zag from the once delooped space of pseudoisotopies of a closed 2n-disc...
Cataloged from PDF version of article.A classical conjecture in transformation group theory states t...
We construct certain unstable higher-order homotopy operations indexed by the simplex categories of ...
Here the existence of a new homomorphism $P_{\omega} : \Theta_{\mathbb{Z}}^3 \to \mathbb{Z}$ is prov...