Zobrazeno 1 - 10
of 298
pro vyhledávání: '"Quigley, J. D."'
Tambara functors are the analogue of commutative rings in equivariant algebra. Nakaoka defined ideals in Tambara functors, leading to the definition of the Nakaoka spectrum of prime ideals in a Tambara functor. In this work, we continue the study of
Externí odkaz:
http://arxiv.org/abs/2410.23052
Autor:
Bobkova, Irina, Quigley, J. D.
We produce a new $192$-periodic infinite family of simple $\eta$-torsion elements in the stable homotopy groups of spheres using the $\mathit{tmf}$-Hurewicz homomorphism and the complex projective plane.
Comment: 4 pages. Comments welcome!
Comment: 4 pages. Comments welcome!
Externí odkaz:
http://arxiv.org/abs/2410.21181
We compute Mackey functor-valued Tor over certain free incomplete Tambara functors, generalizing the computation of Tor over a polynomial ring on one generator. In contrast with the classical situation where the resulting Tor groups vanish above degr
Externí odkaz:
http://arxiv.org/abs/2410.11974
In equivariant algebra, Mackey functors replace abelian groups and incomplete Tambara functors replace commutative rings. In this context, we prove that equivariant Hochschild homology can sometimes be computed using Mackey functor-valued Tor. To com
Externí odkaz:
http://arxiv.org/abs/2407.18382
We identify seven new $192$-periodic infinite families of elements in the $2$-primary stable homotopy groups of spheres. Although their Hurewicz image is trivial for topological modular forms, they remain nontrivial after $\mathrm{T}(2)$- as well as
Externí odkaz:
http://arxiv.org/abs/2404.10062
McDuff and Segal proved that unordered configuration spaces of open manifolds satisfy homological stability: there is a stabilization map $\sigma: C_n(M)\to C_{n+1}(M)$ which is an isomorphism on $H_d(-;\mathbb{Z})$ for $n\gg d$. For a finite group $
Externí odkaz:
http://arxiv.org/abs/2311.02459
Autor:
Botvinnik, Boris, Quigley, J. D.
We deduce the existence of smooth $U(1)$- and $Sp(1)$-actions on certain exotic spheres using complex and quaternionic analogues of the Mahowald {(root)} invariant. In particular, we prove that the complex (respectively, quaternionic) Mahowald invari
Externí odkaz:
http://arxiv.org/abs/2309.04275
We identify the motivic $KGL/2$-local sphere as the fiber of $\psi^3-1$ on $(2,\eta)$-completed Hermitian $K$-theory, over any base scheme containing $1/2$. This is a motivic analogue of the classical resolution of the $K(1)$-local sphere, and extend
Externí odkaz:
http://arxiv.org/abs/2307.13512
Autor:
Kong, Hana Jia, Quigley, J. D.
We compute the slice spectral sequence for the motivic stable homotopy groups of $L$, a motivic analogue of the connective $K(1)$-local sphere over prime fields of characteristic not two. Together with the analogous computation over algebraically clo
Externí odkaz:
http://arxiv.org/abs/2209.08603
Autor:
Quigley, J. D.
Classical work of Lee, Schultz, and Stolz relates the smooth transformation groups of exotic spheres to the stable homotopy groups of spheres. In this note, we apply recent progress on the latter to produce smooth circle and cyclic group actions on c
Externí odkaz:
http://arxiv.org/abs/2209.01591