Ruizhi Huang

activity

20172026

(2 n - 2)

-connected

(4 n - 1)

-dimensional Poincaré Duality complexes

10 citations · 55 across the 25 of their papers we have counts for

collaborators

25 papers

math.AT2026

A Classification of Self-Maps of Generalized Grassmannians

Haibao Duan, Ruizhi Huang, Xuezhi Zhao

Generalized Grassmannians form a fundamental class of flag manifolds associated with Lie groups. The purpose of this paper is to classify self-maps of generalized Grassmannians of…

math.AT2026

On the degrees of equivariant maps from spheres to complex Stiefel manifolds

Haibao Duan, Ruizhi Huang

We study the set of degrees of $Z / m$ -equivariant maps from spheres to complex Stiefel manifolds, motivated by the work of Astey--Gitler--Micha--Pastor. Under a suitable ar…

math.AT2023

Homotopy of blow ups after looping

Ruizhi Huang, Stephen Theriault

The homotopy theory of the blow up construction in algebraic and symplectic geometry is investigated via two approaches. The first approach introduces and develops fibrewise surger…

math.AT2023★ 2 cited

Some asymptotic formulae for torsion in homotopy groups

Guy Boyde, Ruizhi Huang

Inspired by a remarkable work of Félix, Halperin and Thomas on the asymptotic estimation of the ranks of rational homotopy groups, and more recent works of Wu and the authors on lo…

math.AT2022

Sphere bundles over $4$ -manifolds are trivial after looping

Ruizhi Huang

We show that except two special cases, the sphere bundle of a vector bundle over a simply connected $4$ -manifold splits after looping. In particular, this implies that though there…

math.AT2022

Suspension Splitting and Cohomotopy Sets of Simply Connected $7$ -manifolds

Ruizhi Huang, Pengcheng Li

Let $M$ be a closed simply connected $7$ -manifold. In this paper we establish homotopy decompositions of the reduced suspension space $Σ M$ into a wedge sum of simpler spaces when l…

math.AT2022

Homotopy of manifolds stabilized by projective spaces

Ruizhi Huang, Stephen Theriault

We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typical way to stabilize manifolds. In particular, we show a loop homotopy decompositi…

math.AT2022

Fractional structures on bundle gerbe modules and fractional classifying spaces

Fei Han, Ruizhi Huang, Varghese Mathai

We study the homotopy aspects of the twisted Chern classes of torsion bundle gerbe modules. Using Sullivan's rational homotopy theory, we realize the twisted Chern classes at the l…

math.AT2021★ 1 cited

Homotopy theoretic properties of open books

Ruizhi Huang, Stephen Theriault

We study the homotopy groups of open books in terms of those of their pages and bindings. Under homotopy theoretic conditions on the monodromy we prove an integral decomposition re…

math.AT2021

Orders of the canonical vector bundles over configuration spaces of finite graphs

Frederick R. Cohen, Ruizhi Huang

We prove that the order of the canonical vector bundle over the configuration space is $2$ for a general planar graph, and is $4$ for a nonplanar graph.

math.AT2021

Elliptic genus and string cobordism at dimension $24$

Fei Han, Ruizhi Huang

It is known that spin cobordism can be determined by Stiefel-Whitney numbers and index theory invariants, namely $K O$ -theoretic Pontryagin numbers. In this paper, we show that stri…

math.AT2021

Coformality around fibrations and cofibrations

Ruizhi Huang

We show that in a fibration the coformality of the base space implies the coformality of the total space under reasonable conditions, and these conditions can not be weakened. The…

math.AT2021★ 10 cited

Loop space decompositions of $(2 n - 2)$ -connected $(4 n - 1)$ -dimensional Poincaré Duality complexes

Ruizhi Huang, Stephen Theriault

Beben and Wu showed that if $M$ is a $(2 n - 2)$ -connected $(4 n - 1)$ -dimensional Poincaré Duality complex such that $n \geq 3$ and $H^{2 n} (M; Z)$ consists only of odd torsion, t…

math.AT2021★ 4 cited

Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups

Ruizhi Huang, Stephen Theriault

Using integral methods we recover and generalize some results by Félix, Halperin and Thomas on the growth of the rational homology groups of free loop spaces, and obtain a new fami…

math.AT2021★ 5 cited

Loop homotopy of $6$ -manifolds over $4$ -manifolds

Ruizhi Huang

Let $M$ be the $6$ -manifold $M$ as the total space of the sphere bundle of a rank $3$ vector bundle over a simply connected closed $4$ -manifold. We show that after looping $M$ is h…

math.AT2021★ 7 cited

Suspension homotopy of $6$ -manifolds

Ruizhi Huang

For a simply connected closed orientable manifold of dimension $6$ , we show its homotopy decomposition after double suspension. This allows us to determine its $K$ - and $K O$ -groups…

math.AT2021★ 3 cited

On characteristic numbers of $24$ dimensional String manifolds

Fei Han, Ruizhi Huang

In this paper, we study the Pontryagin numbers of $24$ dimensional String manifolds. In particular, we find representatives of an integral basis of the String cobrodism group at di…

math.DG2020★ 5 cited

Cubic forms, anomaly cancellation and modularity

Fei Han, Ruizhi Huang, Kefeng Liu +1

Motivated by the cubic forms and anomaly cancellation formulas of Witten-Freed-Hopkins, we give some new cubic forms on spin, spin $^{c}$ , spin $^{w_{2}}$ and orientable 12-manifolds res…

math.AT2019

String $^{c}$ Structures and Modular Invariants

Haibao Duan, Fei Han, Ruizhi Huang

In this paper, we study some algebraic topology aspects of String $^{c}$ structures, more precisely, from the perspective of Whitehead tower and the perspective of the loop group of $…

math.AT2018★ 1 cited

Homotopy types of gauge groups over high dimensional manifolds

Ruizhi Huang

The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high dimensional man…

math.AT2018

Homotopy of gauge groups over non-simply-connected five dimensional manifolds

Ruizhi Huang

Both the gauge groups and $5$ -manifolds are important in physics and mathematics. In this paper, we combine them together to study the homotopy aspects of gauge groups over $5$ -man…

math.AT2017★ 9 cited

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 $p$ -local complexes, and define a space to be locally hyperbolic if its homotopy groups have expo…

math.AT2017★ 6 cited

Cancellation and homotopy rigidity of classical functors

Ruizhi Huang, Jie Wu

We first show that simply connected co- $H$ -spaces and connected $H$ -spaces can be uniquely decomposed into prime factors in the homotopy category of pointed $p$ -local spaces of fin…

math.AT2017★ 2 cited

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…

A Classification of Self-Maps of Generalized Grassmannians

On the degrees of equivariant maps from spheres to complex Stiefel manifolds

Homotopy of blow ups after looping

Some asymptotic formulae for torsion in homotopy groups

Sphere bundles over 4-manifolds are trivial after looping

Suspension Splitting and Cohomotopy Sets of Simply Connected 7-manifolds

Homotopy of manifolds stabilized by projective spaces

Fractional structures on bundle gerbe modules and fractional classifying spaces

Homotopy theoretic properties of open books

Orders of the canonical vector bundles over configuration spaces of finite graphs

Elliptic genus and string cobordism at dimension 24

Coformality around fibrations and cofibrations

Loop space decompositions of (2n−2)-connected (4n−1)-dimensional Poincaré Duality complexes

Exponential growth in the rational homology of free loop spaces and in torsion homotopy groups

Loop homotopy of 6-manifolds over 4-manifolds

Suspension homotopy of 6-manifolds

On characteristic numbers of 24 dimensional String manifolds

Cubic forms, anomaly cancellation and modularity

Stringc Structures and Modular Invariants

Homotopy types of gauge groups over high dimensional manifolds

Homotopy of gauge groups over non-simply-connected five dimensional manifolds

Exponential growth of homotopy groups of suspended finite complexes

Cancellation and homotopy rigidity of classical functors

Combinatorics of double loop suspensions, evaluation maps and Cohen groups

Sphere bundles over $4$ -manifolds are trivial after looping

Suspension Splitting and Cohomotopy Sets of Simply Connected $7$ -manifolds

Elliptic genus and string cobordism at dimension $24$

Loop space decompositions of $(2 n - 2)$ -connected $(4 n - 1)$ -dimensional Poincaré Duality complexes

Loop homotopy of $6$ -manifolds over $4$ -manifolds

Suspension homotopy of $6$ -manifolds

On characteristic numbers of $24$ dimensional String manifolds

String $^{c}$ Structures and Modular Invariants