64 citations · 420 across the 98 of their papers we have counts for
52 papers · 1 filter
On the Homotopy Groups of the Suspended Quaternionic Projective Plane and Applications
Juxin Yang, Juno Mukai, Jie Wu
In this paper, we determined the -components of the homotopy groups for all and all , especially for the unstable on…
On the Cayley-persistence algebra
Wanying Bi, Jingyan Li, Jian Liu +1
In this paper, we introduce a persistent (co)homology theory for Cayley digraph grading. We give the algebraic structures of Cayley-persistence object. Specifically, we consider th…
On Modular Cohomotopy Groups
Pengcheng Li, Jianzhong Pan, Jie Wu
Let be a prime and let be the set of homotopy classes of based maps from CW-complexes into the mod Moore spaces $M_n(\…
The Embedded Homology of Hypergraph Pairs
Shiquan Ren, Jie Wu, Mengmeng Zhang
In this paper, we generalize the embedded homology groups of hypergraphs initially given in [S. Bressan, J. Li, S. Ren, and J. Wu, The embedded homology of hypergraphs and applicat…
Cohomology ring of manifold arrangements
Junda Chen, Zhi Lü, Jie Wu
We study the cohomology ring of the complement of a manifold arrangement in a smooth manifold without boundary. We first give the conce…
The stability of persistent homology of hypergraphs
Shiquan Ren, Jie Wu
Hypergraph is the most general model for complex networks involving group interactions. Taking the ideas of path homology from Alexander Grigor'yan, Yong Lin, Yuri Muranov and Shin…
Weighted Path homology of Weighted Digraphs and Persistence
Yong Lin, Shiquan Ren, Chong Wang +1
In recent years, A. Grigor'yan, Y. Lin, Y. Muranov and S.T. Yau [6, 7, 8, 9] constructed a path homology theory for digraphs. Later, S. Chowdhury and F. Memoli [3] studied the pers…
Discrete Morse Theory for Weighted Simplicial Complexes
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we study Forman's discrete Morse theory in the context of weighted homology. We develop weighted versions of classical theorems in discrete Morse theory. A key diffe…
On homotopy aspects and cablings of virtual pure braid groups
Valeriy G. Bardakov, Roman Mikhailov, Jie Wu
By exploring simplicial structure of pure virtual braid groups, we give new connections between the homotopy groups of the 3-sphere and the virtual braid groups that are related to…
Weighted Fundamental Group
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to th…
Hodge Decompositions for Weighted Hypergraphs
Shiquan Ren, Chengyuan Wu, Jie Wu
Weighted hypergraphs are generalizations of weighted simplicial complexes. In recent years, weighted Laplacians of weighted simplicial complexes have been studied. In 2016, as a ge…
A Discrete Morse Theory for Hypergraphs
Shiquan Ren, Chong Wang, Chengyuan Wu +1
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. By [11], a hypergraph gives an associated simplicial complex. By [4], the embedded ho…
Weighted (Co)homology and Weighted Laplacian
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we generalize the combinatorial Laplace operator of Horak and Jost by introducing the -weighted coboundary operator induced by a weight function . Our weight f…
Maps on random hypergraphs and random simplicial complexes
Shiquan Ren, Chengyuan Wu, Jie Wu
Let be a simplicial complex. In this paper, we study random sub-hypergraphs and random sub-complexes of . By considering the minimal complex that a sub-hypergraph can be emb…
Computational Tools in Weighted Persistent Homology
Shiquan Ren, Chengyuan Wu, Jie Wu
In this paper, we study further properties and applications of weighted homology and persistent homology. We introduce the Mayer-Vietoris sequence and generalized Bockstein spectra…
Weighted Persistent Homology
Shiquan Ren, Chengyuan Wu, Jie Wu
In this paper we develop the theory of weighted persistent homology. In 1990, Robert J. Dawson was the first to study in depth the homology of weighted simplicial complexes. We gen…
Exponential growth of homotopy groups of suspended finite complexes
Ruizhi Huang, Jie Wu
We study the asymptotic behavior of the homotopy groups of simply connected finite -local complexes, and define a space to be locally hyperbolic if its homotopy groups have expo…
Cancellation and homotopy rigidity of classical functors
Ruizhi Huang, Jie Wu
We first show that simply connected co--spaces and connected -spaces can be uniquely decomposed into prime factors in the homotopy category of pointed -local spaces of fin…
Combinatorics of double loop suspensions, evaluation maps and Cohen groups
Ruizhi Huang, Jie Wu
We reformulate Milgram's model of a double loop suspension in terms of a preoperad of posets, each stage of which is the poset of all ordered partitions of a finite set. Using this…
Cobordism classes of maps and covers for spheres
Oleg R. Musin, Jie Wu
In this paper we show that for m>n the set of cobordism classes of maps from m-sphere to n-sphere is trivial. The determination of the cobordism homotopy groups of spheres admits a…
Computing the Homology of Hypergraphs
Shiquan Ren, Chengyuan Wu, Stephane Bressan +1
Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have be…
Simplicial James-Hopf map and decompositions of the unstable Adams spectral sequence for suspensions
Fedor Pavutnitskiy, Jie Wu
We use combinatorial group theory methods to extend the definition of a classical James-Hopf invariant to a simplicial group setting. This allow us to realize certain coalgebra ide…
On -spaces
Ruizhi Huang, Jie Wu
We prove a necessary condition for the existence of the -structure on spaces, and also derive a simple proof for the finiteness of the number of $A…
The Embedded Homology of Hypergraphs and Applications
Stephane Bressan, Jingyan Li, Shiquan Ren +1
Hypergraphs are mathematical models for many problems in data sciences. In recent decades, the topological properties of hypergraphs have been studied and various kinds of (co)homo…