Tootfinder

Compactly supported $\mathbb{A}^1$-Euler characteristics of symmetric powers of cellular varieties
Jesse Pajwani, Herman Rohrbach, Anna M. Viergever
https://arxiv.org/abs/2404.08486

Compactly supported $\mathbb{A}^1$-Euler characteristics of symmetric powers of cellular varieties
The compactly supported $\mathbb{A}^1$-Euler characteristic, introduced by Hoyois and later refined by Levine and others, is an anologue in motivic homotopy theory of the classical Euler characteristic of complex topological manifolds. It is an invariant on the Grothendieck ring of varieties $\mathrm{K}_0(\mathrm{Var}_k)$ taking values in the Grothendieck-Witt ring $\mathrm{GW}(k)$ of the base field $k$. The former ring has a natural power structure induced by symmetric powers of varieties. In …

This https://arxiv.org/abs/2309.07169 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Spectral Convergence of Simplicial Complex Signals
Topological signal processing (TSP) utilizes simplicial complexes to model structures with higher order than vertices and edges. In this paper, we study the transferability of TSP via a generalized higher-order version of graphon, known as complexon. We recall the notion of a complexon as the limit of a simplicial complex sequence [1]. Inspired by the graphon shift operator and message-passing neural network, we construct a marginal complexon and complexon shift operator (CSO) according to comp…

This https://arxiv.org/abs/2402.09798 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Oka-1 manifolds: New examples and properties
In this paper we investigate Oka-1 manifolds and Oka-1 maps, a class of complex manifolds and holomorphic maps recently introduced by Alarcón and Forstnerič. Oka-1 manifolds are characterised by the property that holomorphic maps from any open Riemann surface to the manifold satisfy the Runge approximation and Weierstrass interpolation conditions, while Oka-1 maps enjoy similar properties for liftings of maps from open Riemann surfaces in the absence of topological obstructions. We also formu…

This https://arxiv.org/abs/2212.12225 has been replaced.
link: https://scholar.google.com/scholar?q=a

Hyperbolicity and fundamental groups of complex quasi-projective varieties
This paper investigates the relationship between the hyperbolicity of complex quasi-projective varieties $X$ and the (topological) fundamental group $π_1(X)$ in the presence of a linear representation $\varrho: π_1(X) \to {\rm GL}_N(\mathbb{C})$. We present our main results in three parts. Firstly, we show that if $\varrho$ is bigand the Zariski closure of $\varrho(π_1(X))$ semisimple, then for any $X^σ:=X\times_σ\mathbb{C}$ where $σ\in {\rm Aut}(\mathbb{C}/\mathbb{Q})$, there exists a …

This https://arxiv.org/abs/2304.13716 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Fermionic skyrmions and bosonization for a Gross-Neveu transition
We investigate a 2+1-D interacting Dirac semimetal with onsite flavor SU(2) symmetry. Topological considerations imply that the skyrmions in the flavor-symmetry-breaking phase carry electron quantum numbers, motivating a dual bosonized low energy description in terms of two complex scalars coupled to an abelian Chern-Simons field. We propose that the transition between a nearby Chern insulator and the flavor symmetry-broken phase is a bicritical point in the bosonized description, and also sugg…

Exploring Homological Properties of Independent Complexes of Kneser Graphs
Ziqin Feng, Guanghui Wang
https://arxiv.org/abs/2404.10566 https://

Exploring Homological Properties of Independent Complexes of Kneser Graphs
We discuss the topological properties of the independence complex of Kneser graphs, Ind(KG$(n, k))$, with $n\geq 3$ and $k\geq 1$. By identifying one kind of maximal simplices through projective planes, we obtain homology generators for the $6$-dimensional homology of the complex Ind(KG$(3, k))$. Using cross-polytopal generators, we provide lower bounds for the rank of $p$-dimensional homology of the complex Ind(KG$(n, k))$ where $p=1/2\cdot {2n+k\choose 2n}$. Denote $\mathcal{F}_n^{[m]}$ to …

This https://arxiv.org/abs/2309.07169 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Spectral Convergence of Complexon Shift Operators
Topological Signal Processing (TSP) utilizes simplicial complexes to model structures with higher order than vertices and edges. In this paper, we study the transferability of TSP via a generalized higher-order version of graphon, known as complexon. We recall the notion of a complexon as the limit of a simplicial complex sequence [1]. Inspired by the graphon shift operator and message-passing neural network, we construct a marginal complexon and complexon shift operator (CSO) according to comp…

This https://arxiv.org/abs/2403.08116 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cyclic homology of categorical coalgebras and the free loop space
We prove that the cyclic chain complex of the categorical coalgebra of singular chains on an arbitrary topological space $X$ is naturally quasi-isomorphic to the $S^1$-equivariant chains of the free loop space of $X$. This statement does not require any hypotheses on $X$ or on the commutative ring of coefficients. Along the way, we introduce a family of polytopes, coined as Goodwillie polytopes, that controls the combinatorics behind the relationship of the coHochschild complex of a categorical…

Exploring Homological Properties of Independent Complexes of Kneser Graphs
Ziqin Feng, Guanghui Wang
https://arxiv.org/abs/2404.10566 https://

Exploring Homological Properties of Independent Complexes of Kneser Graphs
We discuss the topological properties of the independence complex of Kneser graphs, Ind(KG$(n, k))$, with $n\geq 3$ and $k\geq 1$. By identifying one kind of maximal simplices through projective planes, we obtain homology generators for the $6$-dimensional homology of the complex Ind(KG$(3, k))$. Using cross-polytopal generators, we provide lower bounds for the rank of $p$-dimensional homology of the complex Ind(KG$(n, k))$ where $p=1/2\cdot {2n+k\choose 2n}$. Denote $\mathcal{F}_n^{[m]}$ to …