相关论文: The Viterbo Transfer as a Map of Spectra

A planar stuffed map is an embedding of a graph into the 2-sphere $S^{2}$, considered up to orientation-preserving homeomorphisms, such that the complement of the graph is a collection of disjoint topologically connected components that are…

Previous work constructed a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 as an E_infinity-ring spectrum, based on the study of elliptic curves with level-3 structure. We show that the natural map…

For a graph $G(V,E)$ and $l \in \mathbb{N}$, an $l$ distance coloring is a coloring $f: V \to \{1, 2, \cdots, n\}$ of $V$ such that $\forall u,\;v \in V,\; u\neq v,\; f(u)\neq f(v)$ when $d(u,v) \leq l$. Here $d(u,v)$ is the distance…

We construct the vortex Floer homology group $VHF (M,\mu;H)$ for an aspherical Hamiltonian $G$-manifold $(M, \omega)$ with moment map $\mu$ and a class of $G$-invariant Hamiltonian loop $H_t$, following the proposal of [3]. This is a…

We use the transfer matrix formalism for dimers proposed by Lieb, and generalize it to address the corresponding problem for arrow configurations (or trees) associated to dimer configurations through Temperley's correspondence. On a…

Let $X^{n}$ be an arbitrary oriented closed generalized $n$-manifold, $n\ge 5$. In our recent paper (Proc. Edinb. Math. Soc. (2) 63 (2020), no. 2, 597-607) we have constructed a map $t:\mathcal{N}(X^{n}) \to H^{st}_{n} ( X^{n};…

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series…

How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…

A semiclassical model is presented for characterizing the linear response of elementary quantum optical systems involving cavities, optical fibers, and atoms. Formulating the transmission and reflection spectra using a scattering-wave…

The signature of a closed manifold is an important geometric topology. Let $M$ be a closed manifold and $N$ be a codimension 2 submanifold of it. Given certain homotopy conditions, Higson, Xie and Schick proved an invariance theorem in…

We address various topologies (de Bruijn, chordal ring, generalized Petersen, meshes) in various ways ( isometric embedding, embedding up to scale, embedding up to a distance) in a hypercube or a half-hypercube. Example of obtained…

Let $G$ be a reductive group over a local field $F$ and let $\rho:{}^LG \to \mathrm{GL}_{V_{\rho}}(\mathbb{C})$ be a representation of its $L$-group satisfying suitable assumptions. Braverman, Kazhdan and Ng\^o conjectured that one has a…

For a closed 4-manifold X and closed 3-manifold M we investigate the smallest integer n (perhaps infinity) such that M embeds in the connected sum of n copies of X. It is proven that any lens space (or homology lens space) embeds…

Transfer maps and projection formulas are undoubtedly one of the key tools in the development and computation of (co)homology theories. In this note we develop an unified treatment of transfer maps and projection formulas in the…

Graph embedding is a powerful method in parallel computing that maps a guest network $G$ into a host network $H$. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion and the…

We introduce the relation ${\rho}_{\lambda}$-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives, and present some of its essential properties. Among other things, we give…

The goal of this paper is to set up the general framework of higher-dimensional Heegaard Floer homology, define the contact class, and use it to give an obstruction to the Liouville fillability of a contact manifold and a sufficient…

We introduce a notion of approximate orthogonality preserving mappings between Hilbert $C^*$-modules. We define the concept of $(\delta, \varepsilon)$-orthogonality preserving mapping and give some sufficient conditions for a linear mapping…

We construct a stable infinity category with objects flow categories and morphisms flow bimodules; our construction has many flavors, related to a choice of bordism theory, and we discuss in particular framed bordism and the bordism theory…

In deep learning, transfer learning (TL) has become the de facto approach when dealing with image related tasks. Visual features learnt for one task have been shown to be reusable for other tasks, improving performance significantly. By…