세미나/포럼
[세미나/포럼] [2019.01.24-25.목-금] 수학과 위상조합세미나 개최 안내
- 세미나/포럼
- 교내
- 박수현
- 2019-01-21
안녕하세요. 아주대 위상조합 세미나를 아래와 같이 개최하고자 합니다.
많은 참여부탁드립니다.
제목 : Simplicial cohomology and topology of real toric manifolds
연사 : Hanchul Park (Jeju National University)
일시 : 1월 24-25일 목-금요일 15:00 ~ 16:00
장소 : 팔달관 621호
초록 :
Toric topology is the study of topological spaces with particularly good torus symmetry. Those spaces, called (real) toric spaces, can be represented by a simplicial sphere $K$ and additional combinatorial information. Real toric manifolds and real moment-angle manifolds are examples of real toric spaces.
The topology of the real toric manifold $M^\mathbb{R}$ has been less known than that of its complex counterpart. In 1985, Jurkiewicz gave the formula for the $\mathbb{Z}_2$-cohomology ring of $M^\mathbb{R}$. Its $\mathbb{Q}$-Betti numbers were calculated by Suciu and Trevisan in their unpublished paper, and the result was strengthened for coefficient ring $R$ in which 2 is a unit by Suyoung Choi and the speaker.
In this series of talks, we study the cup product for $H^*(M^\mathbb{R};R)$ recently computed by Choi and the speaker. To do this, we briefly review simplicial (co)homology and Hochster formula for real moment-angle complexes, and explain the method to compute the cup product using the simplicial cohomology.