中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

拓扑研讨班

Speaker: 肖咏涵 (北京大学)

Inviter: 李振坤

Language: Chinese

Title: The equivalence between two real Seiberg-Witten-Floer homologies

Time & Venue: 2026年1月7日（星期三）14: 30-15: 30 & N820

Abstract: Recently, 3&4 manifolds with finite group actions has become a popular topic. Real manifolds form the simplest class among them. Following the strategy of Manolescu, Kronheimer-Mrowka, respectively, Konno-Miyazawa-Taniguchi and Li introduced two versions of real Seiberg-Witten-Floer homologies and developed many interesting applications. In this work, we show the two homology theories are equivalence whenever they are both defined following the strategy developed by Lidman and Manolescu. As application, we identify Froyshov-type invariants from two theories and proved some Smith-type inequalities. In this talk, we first review the two approaches to (real) Seiberg-Witten-Floer homologies, then sketch a proof of our main theorem. If time admits, we talk about the applications and some basic examples.