相关论文: A $v_1$-banded vanishing line for the mod 2 Moore …

In 1974, Gugenheim and May showed that the cohomology $\text{Ext}_A(R,R)$ of a connected augmented algebra over a field $R$ is generated by elements with $s = 1$ under matric Massey products. In particular, this applies to the $E_2$ page of…

We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We show that if X is a smooth affine scheme of dimension d over a field k of finite 2-cohomological dimension (with char(k)…

We compute the mod $2$ homology of the spectrum $\mathrm{tmf}$ of topological modular forms by proving a 2-local equivalence $\mathrm{tmf} \wedge DA(1) \simeq \mathrm{tmf}_1(3) \simeq BP\left \langle 2\right\rangle$, where $DA(1)$ is an…

We compute the mod-2 connected KU-homology of the Eilenberg-MacLane space K(Z/2,2), using a novel Adams spectral sequence analysis.

In this paper we give top most and least indices of non vanishing cohomology modules of line bundles in the Kac Moody setting in terms of Weyl group combinatorics. We also prove a surjection Theorem.

We prove that the genuine $C_{2^n}$-spectrum $N_{C_{2}}^{C_{2^n}}MU_{\mathbb{R}}$ is cofree, for all $n$. Our proof is a formal argument using chromatic hypercubes and the Slice Theorem of Hill, Hopkins, and Ravenel. We show that this gives…

We study the homotopy type of the harmonic compactification of the moduli space of a 2-cobordism S with one outgoing boundary component, or equivalently of the space of Sullivan diagrams of type S on one circle. Our results are of two…

We describe some periodic structure in the cohomology of the moduli stack of 1-dimensional formal group laws, also known as the $E_2$-page of the classical Adams--Novikov spectral sequence. This structure is distinct from the familiar…

The spectral sequence associated to the Arone-Goodwillie tower for the n-fold loop space functor is used to show that the first two non-trivial layers of the nilpotent filtration of the reduced mod 2 cohomology of a (sufficiently connected)…

We investigate periodic diffeomorphisms of non-compact aspherical manifolds (and orbifolds) and describe a class of spaces that have no homotopically trivial periodic diffeomorphisms. Prominent examples are moduli spaces of curves and…

We make some computations in stable motivic homotopy theory over Spec \mathbb{C}, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct a motivic analogue of the real K-theory spectrum KO. We also…

We make a conjecture about the whole $E_2$ page of the May spectral sequence in terms of generators and relations and we prove it in a subalgebra which covers a large range of dimensions. We show that the $E_2$ page plays a universal role…

We show that up to automorphisms of $\mathbb P^2_{\mathbb C}$ there are $14$ homogeneous convex foliations of degree $5$ on $\mathbb P^2_{\mathbb C}.$ We establish some properties of the Fermat foliation $\mathcal F_{0}^{d}$ of degree…

We study both analytically and numerically the nonlinear stage of the instability of one-dimensional solitons in a small vicinity of the transition point from supercritical to subcritical bifurcations in the framework of the generalized…

We prove Eilenberg-Watts Theorem for 2-categories of the representation categories $\C\x\Mod$ of finite tensor categories $\C$. For a consequence we obtain that any autoequivalence of $\C\x\Mod$ is given by tensoring with a representative…

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 prove that the Clifford spectrum associated to three 2 by 2 matrices is nonempty. The structure of Clifford is described in terms "moving" level curves. We discuss some implication of a conjecture formulated for arbitrary size n by n of…

For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting…

A classical result of Conway and Pless is that a natural projection of the fixed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual. In this paper we prove that the same holds for involutions under…

It is proved that the continuous bounded cohomology of SL_2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low…