Yutao Liu

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20202025

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math.AT2025

Periodicity and finite complexity in higher real $K$ -theories

Zhipeng Duan, Michael A. Hill, Guchuan Li +4

In this paper, we establish periodicity results for higher real $K$ -theories at all heights and for all finite subgroups of the Morava stabilizer group at the prime 2. We further a…

math.AT2022

Computing Equivariant Homotopy with a Splitting Method

Yutao Liu

We develop a new method in the computation of equivariant homotopy, which is based on the splitting of cofiber sequences associated to universal spaces in the category of equivaria…

math.AT2021

Universal Spaces and Splittings of Equivariant Spectra

Yutao Liu

Let $G$ be a finite group. We re-analyze the splitting of rational $G$ -spectra, which is discussed in Barne's thesis and traces back to Greenlees and May. We will study how the spl…

math.AT2020

Twisted Bar Construction

Yutao Liu

This is an expository paper about a $C_{2}$ -equivariant analog of the bar construction. We will explain its construction and prove how it acts as a $σ$ -fold delooping machi…

Periodicity and finite complexity in higher real K-theories

Computing Equivariant Homotopy with a Splitting Method

Universal Spaces and Splittings of Equivariant Spectra

Twisted Bar Construction

Periodicity and finite complexity in higher real $K$ -theories