The C2–spectrum Tmf1 (3) and its invertible modules
We explore the C 2–equivariant spectra Tmf 1 (3) and TMF 1 (3). In particular, we compute
their C 2–equivariant Picard groups and the C 2–equivariant Anderson dual of Tmf 1 (3) …
their C 2–equivariant Picard groups and the C 2–equivariant Anderson dual of Tmf 1 (3) …
The 2–primary Hurewicz image of tmf
M Behrens, M Mahowald, JD Quigley - Geometry & Topology, 2023 - msp.org
We determine the image of the 2–primary tmf Hurewicz homomorphism, where tmf is the
spectrum of topological modular forms. We do this by lifting elements of tmf∗ to the …
spectrum of topological modular forms. We do this by lifting elements of tmf∗ to the …
Detecting exotic spheres in low dimensions using coker J
Building off of the work of Kervaire–Milnor and Hill–Hopkins–Ravenel, Wang and Xu
showed that the only odd dimensions n for which S n has a unique differentiable structure …
showed that the only odd dimensions n for which S n has a unique differentiable structure …
Adams spectral sequences for non-vector-bundle Thom spectra
When $ R $ is one of the spectra $\mathit {ku} $, $\mathit {ko} $, $\mathit {tmf} $, $\mathit
{MTSpin}^ c $, $\mathit {MTSpin} $, or $\mathit {MTString} $, there is a standard approach to …
{MTSpin}^ c $, $\mathit {MTSpin} $, or $\mathit {MTString} $, there is a standard approach to …
Topological modular and automorphic forms
M Behrens - Handbook of homotopy theory, 2020 - taylorfrancis.com
The spectrum of topological modular forms was first introduced by Hopkins and Miller. This
chapter discusses a class of moduli stacks of abelian varieties which give rise to spectra of …
chapter discusses a class of moduli stacks of abelian varieties which give rise to spectra of …
On the ‐term of the ‐Adams spectral sequence
The E 1‐term of the (2‐local) bo‐based Adams spectral sequence for the sphere spectrum
decomposes into a direct sum of av 1‐periodic part, and av 1‐torsion part. Lellmann and …
decomposes into a direct sum of av 1‐periodic part, and av 1‐torsion part. Lellmann and …
New infinite families in the stable homotopy groups of spheres
P Bhattacharya, I Bobkova, JD Quigley - arXiv preprint arXiv:2404.10062, 2024 - arxiv.org
We identify seven new $192 $-periodic infinite families of elements in the $2 $-primary
stable homotopy groups of spheres, whose images are nontrivial in the $\mathrm {K}(2) $-as …
stable homotopy groups of spheres, whose images are nontrivial in the $\mathrm {K}(2) $-as …
On BP⟨ 2⟩–cooperations
D Culver - Algebraic & Geometric Topology, 2019 - msp.org
We develop techniques to compute the cooperations algebra for the second truncated
Brown–Peterson spectrum BP〈 2〉. We prove that the cooperations algebra BP〈 2〉∗ BP〈 …
Brown–Peterson spectrum BP〈 2〉. We prove that the cooperations algebra BP〈 2〉∗ BP〈 …
[PDF][PDF] The structure of the v_2-local algebraic tmf resolution
M Behrens, P Bhattacharya, D Culver - arXiv preprint arXiv:2301.11230, 2023 - arxiv.org
arXiv:2301.11230v1 [math.AT] 26 Jan 2023 Page 1 THE STRUCTURE OF THE v2-LOCAL
ALGEBRAIC tmf RESOLUTION M. BEHRENS, P. BHATTACHARYA, AND D. CULVER Abstract …
ALGEBRAIC tmf RESOLUTION M. BEHRENS, P. BHATTACHARYA, AND D. CULVER Abstract …
Endotrivial modules for the quaternion group and iterated Jokers in chromatic homotopy theory
A Baker - arXiv preprint arXiv:2309.05921, 2023 - arxiv.org
The algebraic Joker module was originally described in the 1970s by Adams and Priddy and
is a $5 $-dimensional module over the subHopf algebra $\mathcal {A}(1) $ of the mod~ $2 …
is a $5 $-dimensional module over the subHopf algebra $\mathcal {A}(1) $ of the mod~ $2 …