Related papers: On the nonexistence of Smith-Toda complexes

Persistent homology has emerged as a novel tool for data analysis in the past two decades. However, there are still very few shapes or even manifolds whose persistent homology barcodes (say of the Vietoris-Rips complex) are fully known.…

We study a space of genus $g$ stable, $n$-marked tropical curves with total edge length $1$. Its rational homology is identified both with top-weight cohomology of the complex moduli space $M_{g,n}$ and with the homology of a marked version…

We construct a finite 1-connected CW complex X such that $H_*(\Omega X; Z)$ has p-torsion for the infinitely many primes satisfying p ~ 5,7,17,19 mod 24, but no p-torsion for the infinitely many primes satisfying p ~ 13 or 23 mod 24.

For an appropriate choice of a $\mathbb{Z}$-grading structure, we prove that the wrapped Fukaya category of the symmetric square of a $(k+3)$-punctured sphere, i.e. the Weinstein manifold given as the complement of $(k+3)$ generic lines in…

Given a grid diagram for a knot or link K in $S^3$, we construct a filtered spectrum whose homology is the knot Floer homology of K. We conjecture that the filtered homotopy type of the spectrum is an invariant of K. Our construction does…

In this paper we constructs a new nontrivial family in the stable homotopy groups of spheres $\pi_{p^nq+2pq+q-3}S$ which is of order $p$ and is represented by $k_0h_{n} \in Ext_A^{3,p^nq+2pq+q}(\mathbb{Z}_p,\mathbb{Z}_p)$ in the Adams…

We prove that any K(n)-acyclic, $D_p$-ring spectrum is K(n+1)-acyclic, affirming an old conjecture of Mark Hovey.

Building on work of Stolz, we prove for integers $0 \le d \le 3$ and $k>232$ that the boundaries of $(k-1)$-connected, almost closed $(2k+d)$-manifolds also bound parallelizable manifolds. Away from finitely many dimensions, this settles…

We formulate a conjecture that arithmetic locally symmetric manifolds have simple homotopy type, and prove it for the non-compact case. More precisely, we show that, for any symmetric space S of non-compact type without Euclidean de Rham…

The complete spectrum of D=6, N=4b supergravity with n tensor multiplets compactified on AdS_3 x S^3 is determined. The D=6 theory obtained from the K_3 compactification of Type IIB string requires that n=21, but we let n be arbitrary. The…

Let $\Tt$ be an aperiodic and repetitive tiling of $\RM^d$ with finite local complexity. We present a spectral sequence that converges to the $K$-theory of $\Tt$ with $E_2$-page given by a new cohomology that will be called PV in reference…

In this note, we fill in a gap in the literature by proving that the Teichmueller modular groups (mapping class groups) are not Poincare duality groups and the complexes of curves of surfaces have infinite homotopy type (i.e. are not…

We develop an extension of the usual theory of formal group laws where the base ring is not required to be commutative and where the formal variables need neither be central nor have to commute with each other. We show that this is the…

We build a new spectrum of recursive models (SRM(T)) of a strongly minimal theory. This theory is non-disintegrated, flat, model complete, and in a language with a finite signature.

It is proved that self-gravitating static scalar fields whose self-interaction potential $V(\psi^2)$ is a monotonically increasing function of its argument cannot form spherically symmetric asymptotically flat bound matter configurations.…

This is an exposition of facts about p-local spectra, p-complete spectra and modules over the p-complete sphere spectrum, including homological criteria for finiteness. Most things are well-known to the experts, with a couple of potential…

Let R be a commutative ring with unity and M be an R-module. In this study, we construct the \tilde{Spec}(M) topology using the prime spectrum of module M and multiplicatively closed subsets of R with the closed sets \tilde{V}(S)={P \in…

It has been suggested that non-invertible symmetry protected topological phases (SPT), due to the lack of a stacking structure, do not have symmetric entanglers (globally symmetric finite-depth quantum circuits) connecting them. Using…

We present upper and lower bounds for symmetrized topological complexity $TC^\Sigma(X)$ in the sense of Basabe-Gonz\'alez-Rudyak-Tamaki. The upper bound comes from equivariant obstruction theory, and the lower bounds from the cohomology of…

The long hunt for a symmetric monoidal category of spectra finally ended in success with the simultaneous discovery of the third author's discovery of symmetric spectra and the Elmendorf-Kriz-Mandell-May category of S-modules. In this paper…