Andrew Senger

activity

20142025

most citedOn the high-dimensional geography problem

6 citations · 13 across the 13 of their papers we have counts for

collaborators

14 papers

math.AT2025

Splitting the Madsen-Tillmann Spectra $M T θ_{n}$

Jonathan Sejr Pedersen, Andrew Senger

We prove that the Madsen-Tillmann spectrum $M T θ_{n}$ splits into the sum of spectra $Σ^{- 2 n} M O ⟨ n + 1 ⟩ \oplus Σ^{\infty - 2 n} R P_{2 n}^{\infty}$ after Postnikov trunct…

math.KT2024

Exact bounds for even vanishing of $K_{*} (Z / p^{n})$

Achim Krause, Andrew Senger

In this note, we prove that $K_{2 i} (Z / p^{n}) \neq = 0$ if and only if $p - 1$ divides $i$ and $0 \leq i \leq (p - 1) p^{n - 2}$ , refining the even vanishing theorem of Antieau, Nik…

math.KT2024

Crystallinity for syntomic cohomology, étale cohomology, and algebraic $K$ -theory

Jeremy Hahn, Ishan Levy, Andrew Senger

We prove for $n \geq c - 1$ that the functor taking an animated ring $R$ to its mod $(p^{c}, v_{1}^{p^{n}})$ syntomic cohomology factors through the functor $R \mapsto R / p^{c (n + 2)}$ , a pheno…

math.AT2023

Examples of disk algebras

Sanath Devalapurkar, Jeremy Hahn, Tyler Lawson +2

We produce refinements of the known multiplicative structures on the Brown--Peterson spectrum $B P$ , its truncated variants $B P ⟨ n ⟩$ , Ravenel's spectra $X (n)$ , and even…

math.GT2022

Inertia groups of $(n - 1)$ -connected $2 n$ -manifolds

Andrew Senger, Adela YiYu Zhang

In this paper, we compute the inertia groups of $(n - 1)$ -connected, smooth, closed, oriented $2 n$ -manifolds where $n \geq 3$ . As a consequence, we complete the diffeomorphism classi…

math.AT2022

Obstruction theory and the level $n$ elliptic genus

Andrew Senger

Given a height $\leq 2$ Landweber exact $E_{\infty}$ -ring $E$ whose homotopy is concentrated in even degrees, we show that any complex orientation of $E$ which satisfies the…

math.AT2022★ 1 cited

How Big are the Stable Homotopy Groups of Spheres?

Robert Burklund, Andrew Senger

In this article we show that the $p$ -torsion exponent of the stable stems grows sublinearly in $n$ and the $p$ -rank of the $E_{2}$ -page of the Adams spectral sequence grows as $\exp(…

math.AT2020★ 1 cited

Galois reconstruction of Artin-Tate $R$ -motivic spectra

Robert Burklund, Jeremy Hahn, Andrew Senger

We explain how to reconstruct the category of Artin-Tate $R$ -motivic spectra as a deformation of the purely topological $C_{2}$ -equivariant stable category. The special fibe…

math.GT2020

Inertia groups in the metastable range

Robert Burklund, Jeremy Hahn, Andrew Senger

We prove that the inertia groups of all sufficiently-connected, high-dimensional $(2 n)$ -manifolds are trivial. This is a key step toward a general classification of manifolds in th…

math.AT2020★ 2 cited

Odd primary analogs of Real orientations

Jeremy Hahn, Andrew Senger, Dylan Wilson

We define, in $C_{p}$ -equivariant homotopy theory for $p > 2$ , a notion of $μ_{p}$ -orientation analogous to a $C_{2}$ -equivariant Real orientation. The definition hinges on a $C_{p}$ -space $…

math.AT2020★ 6 cited

On the high-dimensional geography problem

Robert Burklund, Andrew Senger

In 1962, Wall showed that smooth, closed, oriented, $(n - 1)$ -connected $2 n$ -manifolds of dimension at least $6$ are classified up to connected sum with an exotic sphere by an algebr…

math.AT2019★ 1 cited

On the boundaries of highly connected, almost closed manifolds

Robert Burklund, Jeremy Hahn, Andrew Senger

Building on work of Stolz, we prove for integers $0 \leq d \leq 3$ and $k > 232$ that the boundaries of $(k - 1)$ -connected, almost closed $(2 k + d)$ -manifolds also bound parallelizable ma…

math.AT2017

The Brown-Peterson spectrum is not $E_{2 (p^{2} + 2)}$ at odd primes

Andrew Senger

We show that the odd-primary Brown-Peterson spectrum $BP$ does not admit the structure of an $E_{2 (p^{2} + 2)}$ ring spectrum and that there can be no map $\mathrm{MU…

math.CO2014★ 2 cited

Partition Statistics Equidistributed with the Number of Hook Difference One Cells

Jiaoyang Huang, Andrew Senger, Peter Wear +1

Let $λ$ be a partition, viewed as a Young diagram. We define the hook difference of a cell of $λ$ to be the difference of its leg and arm lengths. Define $h_{1, 1} (λ)$ to be the num…

Splitting the Madsen-Tillmann Spectra MTθn​

Exact bounds for even vanishing of K∗​(Z/pn)

Crystallinity for syntomic cohomology, étale cohomology, and algebraic K-theory

Examples of disk algebras

Inertia groups of (n−1)-connected 2n-manifolds

Obstruction theory and the level n elliptic genus

How Big are the Stable Homotopy Groups of Spheres?

Galois reconstruction of Artin-Tate R-motivic spectra

Inertia groups in the metastable range

Odd primary analogs of Real orientations

On the high-dimensional geography problem

On the boundaries of highly connected, almost closed manifolds

The Brown-Peterson spectrum is not E2(p2+2)​ at odd primes

Partition Statistics Equidistributed with the Number of Hook Difference One Cells

Splitting the Madsen-Tillmann Spectra $M T θ_{n}$

Exact bounds for even vanishing of $K_{*} (Z / p^{n})$

Crystallinity for syntomic cohomology, étale cohomology, and algebraic $K$ -theory

Inertia groups of $(n - 1)$ -connected $2 n$ -manifolds

Obstruction theory and the level $n$ elliptic genus

Galois reconstruction of Artin-Tate $R$ -motivic spectra

The Brown-Peterson spectrum is not $E_{2 (p^{2} + 2)}$ at odd primes