相关论文: The Ando-Hopkins-Rezk orientation is surjective

Given a finite and connected two-dimensional $CW$-complex $K$ with fundamental group $\Pi$ and second integer cohomology group $H^2(K;\mathbb{Z})$ finite of odd order, we prove that: (1) for each local integer coefficient system…

For an $\A^1$-connected pointed simplicial sheaf $\sX$ over a perfect field $k$, we prove that the Hurewicz map $\pi_1^{\A^1}(\sX) \to H_1^{\A^1}(\sX)$ is surjective. We also observe that the Hurewicz map for $\P^1_k$ is the abelianisation…

We present a geometric construction of push-forward maps along projective morphisms for cohomology theories representable in the stable motivic homotopy category assuming that the element corresponding to the stable Hopf map is inverted in…

We calculate the $\eta$-localization of the motivic stable homotopy ring over the complex numbers, confirming a conjecture of Guillou and Isaksen. Our approach is via the motivic Adams-Novikov spectral sequence. In fact, work of Hu, Kriz,…

In this article we investigate a pair of surjective local ring maps $S_1\leftarrow R\to S_2$ and their relation to the canonical projection $R\to S_1\otimes_R S_2$, where $S_1,S_2$ are Tor-independent over $R$. Our main result asserts a…

A continuous surjection $\pi:X\to Y$ between compact Hausdorff spaces induces continuous surjections $\mathcal{M}(\pi)\colon \mathcal{M}(X)\to\mathcal{M}(Y)$ and $\mathcal{H}(\pi): \mathcal{H}(X)\to\mathcal{H}(Y)$ between the spaces of…

The de Rham stack construction of Simpson shows that D-modules are quasicoherent sheaves on a modified geometry. Drinfeld furthermore introduced the ring stack perspective (aka transmutation), which asserts that a coefficient theory is…

For strongly even $\mathbb{E}_{\infty}^{C_2}$-rings $E$ we show that any homotopy ring map $\mathrm{MU} \to E^e$ lifts to an $\mathbb{E}_{\rho}$-map $\mathrm{MU}_{\mathbb{R}} \to E$. This refines the Hahn-Shi Real orientations of Lubin-Tate…

Using techniques introduced by H. Thomas and N. Williams in "Cyclic Symmetry of the Scaled Simplex," we prove that modular sweep maps are bijective. We construct the inverse of the modular sweep map by passing through an intermediary set of…

We show that the topological elliptic genus from the cobordism ring of SU-manifolds to topological Jacobi forms lifts to connective topological Jacobi forms, and that this lift is surjective in homotopy.

In this paper, we proved the existence of Symphonic map from ellipsoid to ellipsoid. We also geive give Hopf construction of Symphonic map from ellipsoid to ellipsoid.

We construct a commutative orthogonal $C_2$-ring spectrum, $\mathrm{MSpin}^c_{\mathbb{R}}$, along with a $C_2$-$E_{\infty}$-orientation $\mathrm{MSpin}^c_{\mathbb{R}} \to \mathrm{KU}_{\mathbb{R}}$ of Atiyah's Real K-theory. Further, we…

Gelfand's trick shows that the spherical Hecke algebra of a $p$-adic split reductive group is commutative. We adapt this strategy in order to show that the spherical derived Hecke algebra is graded-commutative under mild assumptions on the…

We show that a continuous additive positively homogeneous map from a closed not necessarily proper cone in a Banach space onto a Banach space is an open map precisely when it is surjective. This generalization of the usual Open Mapping…

Stasheff showed that if a map between H-spaces is an H-map, then the suspension of the map is extendable to a map between cprojective planes of the H-spaces. Stahseff also proved the converse under the assumption that the multiplication of…

This paper contains a complete computation of the homotopy ring of the spectrum of topological modular forms constructed by Hopkins and Miller. The computation is done away from 6, and at the (interesting) primes 2 and 3 separately, and in…

Working in a generic derived algebro-geometric context, we lay the foundations for the general study of affineness and local descendability. When applied to $\mathbf{E}_\infty$ rings equipped with the fpqc topology, these foundations give…

We show that representations of convolution algebras such as Lustzig's graded affine Hecke algebra or the quiver Hecke algebra and quiver Schur algebra in (affine) type A can be realised in terms of certain equivariant motivic sheaves…

Let S be a compact surface, and M be the double of a handlebody. Given a homotopy class of maps from S to M inducing an isomorphism of fundamental groups, we describe a canonical uniformly lipschitz retraction of the sphere graph of M to…

For the model two-complex $K$ of the group presentation $\mathcal{P}=\langle x,y\,|\,x^{k+1}yxy \rangle$, with $k\geq1$ odd, we describe representatives for all free and based homotopy classes of maps from $K$ into the real projective plane…