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pro vyhledávání: '"Quigley J"'
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
Autor:
Greenlees, J. P. C., Quigley, J. D.
We describe the distribution of infinite groups in the $RO(G)$-graded stable homotopy groups of spheres for a finite group $G$.
Comment: 12 pages, 2 figures. v2: Minor edits. Comments welcome!
Comment: 12 pages, 2 figures. v2: Minor edits. Comments welcome!
Externí odkaz:
http://arxiv.org/abs/2205.02382
We investigate forms of the Hopf invariant one problem in motivic homotopy theory over arbitrary base fields of characteristic not equal to $2$. Maps of Hopf invariant one classically arise from unital products on spheres, and one consequence of our
Externí odkaz:
http://arxiv.org/abs/2112.07479
Autor:
Quigley, J. D., Shah, Jay
We give a new formula for real topological cyclic homology that refines the fiber sequence formula discovered by Nikolaus and Scholze for topological cyclic homology to one involving genuine $C_2$-spectra. To accomplish this, we give a new definition
Externí odkaz:
http://arxiv.org/abs/2112.07462