Details of the Researcher

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Bao Yuanyuan
Section
Graduate School of Information Sciences
Job title
Associate Professor
Degree

  • 博士（理学）（東京工業大学）

  • 修士（理学）（ハルビン工業大学）

  • 修士（理学）（東京工業大学）

Research Interests 1

  • knot, Heegaard Floer homology, gl(1|1)

Research Areas 1

  • Natural sciences / Geometry / Low-dim Topology, Knot theory

Papers 11

  1. $\mathfrak{gl}(1 \vert 1)$-Alexander polynomial for $3$-manifolds International-journal Peer-reviewed

    Yuanyuan Bao, Noboru Ito

    International Journal of Mathematics　34　(4)　2023/04/20

    DOI： 10.1142/S0129167X23500167 　

    ISSN： 0129-167X

  2. Alexander polynomial and spanning trees Peer-reviewed

    Yuanyuan Bao, Zhongtao Wu

    International Journal of Mathematics　32　(08)　2150073-2150073　2021/07

    Publisher: World Scientific Pub Co Pte Lt

    DOI： 10.1142/s0129167x21500737 　

    ISSN： 0129-167X

    eISSN： 1793-6519

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    Inspired by the combinatorial constructions in earlier work of the authors that generalized the classical Alexander polynomial to a large class of spatial graphs with a balanced weight on edges, we show that the value of the Alexander polynomial evaluated at [Formula: see text] gives the weighted number of the spanning trees of the graph.

  3. An Alexander polynomial for MOY graphs Peer-reviewed

    Yuanyuan Bao, Zhongtao Wu

    Selecta Mathematica　26　(2)　2020/05

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s00029-020-00556-8 　

    ISSN： 1022-1824

    eISSN： 1420-9020

  4. A topological interpretation of Viro' gl(1|1)-Alexander polynomial of a graph Peer-reviewed

    Yuanyuan Bao

    Topology and its Applications　267　106870-106870　2019/11

    Publisher: Elsevier BV

    DOI： 10.1016/j.topol.2019.106870 　

    ISSN： 0166-8641

  5. The Heegaard Floer complexes of a trivalent graph defined on two Heegaard diagrams

    Yuanyuan Bao

    2129　69-82　2019/05

  6. Heegaard Floer homology for embedded bipartite graphs

    Yuanyuan Bao

    2004　1-12　2016/05

  7. Polynomial splittings of Ozsv ́ath and Szab ́o’s d-invariant Peer-reviewed

    Yuanyuan Bao

    Topology Proceedings　46　309-322　2015/01

  8. A note on knots with H(2)-unknotting number one Peer-reviewed

    Yuanyuan Bao

    Osaka Journal of Mathematics　51　(3)　585-596　2014/07

  9. On knots having zero negative unknotting number Peer-reviewed

    Yuanyuan Bao

    Indiana University Mathematics Journal　63　(2)　597-613　2014/01

  10. H(2)-unknotting operation related to 2-bridge links Peer-reviewed

    Yuanyuan Bao

    Topology and its Applications　159　(8)　2158-2167　2012/05

    Publisher: Elsevier BV

    DOI： 10.1016/j.topol.2012.02.008 　

    ISSN： 0166-8641

  11. ON THE KNOT FLOER HOMOLOGY OF A CLASS OF SATELLITE KNOTS Peer-reviewed

    YUANYUAN BAO

    Journal of Knot Theory and Its Ramifications　21　(04)　1250030-1250030　2012/04

    Publisher: World Scientific Pub Co Pte Lt

    DOI： 10.1142/s0218216511009807 　

    ISSN： 0218-2165

    eISSN： 1793-6527

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    Knot Floer homology is an invariant for knots in the three-sphere for which the Euler characteristic is the Alexander–Conway polynomial of the knot. The aim of this paper is to study this homology for a class of satellite knots, so as to see how a certain relation between the Alexander–Conway polynomials of the satellite, companion and pattern is generalized on the level of the knot Floer homology. We also use our observations to study a classical geometric invariant, the Seifert genus, of our satellite knots.

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Research Projects 3

  1. gl(1|1)-quantum invariant of trivalent graphs and knot Floer homology

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Early-Career Scientists

    Institution: The University of Tokyo

    2020/04/01 - 2024/03/31

  2. Heegaard Floer homology and its generalization

    BAO Yuanyuan, WU Zhongtao

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Research Activity Start-up

    2014/08/29 - 2016/03/31

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    In the past two years, I studied the Heegaard Floer homology for an embedded bipartite graph in a closed 3-manifold. The Euler characteristic of the homology is the Alexander polynomial, which is a classical invariant in knot theory. During this academic year, my coworker and I found that this polynomial satisfies some relations similar with MOY relations for sl(n) quantum polynomial, and we showed that these relations, in turn, provide a characterization of the Alexander polynomial for a graph. One of the important questions in Heegaard Floer theory is how to understand the theory from the quantum topological viewpoint. In the future, we will study the quantum topological meaning of the Alexander polynomial and then that of its categorification, the Heegaard Floer homology.

  3. 絡み目ホモロジーの位相的な応用

    鮑 園園

    Offer Organization: 日本学術振興会

    System: 科学研究費助成事業

    Category: 特別研究員奨励費

    Institution: 東京工業大学

    2011 - 2012

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    平成24年度の前期,私は主に次の仕事をした.アメリカの数学者Dylan Thurston先生が東京工業大学に訪問した際(2012年4月-6月),私は「bordered Floer homology」を勉強した.Bordered Floer homologyはHeegaard Floer homologyの拡張であり,境界付き3次元多様体の不変量である.Thurston先生がこの理論を作った一人である.そして,8月までに,絡み目のnegative unknotting numberについての論文を一本書き終わった.この結果と結び目同境の関係を説明した.この論文は最近Indiana University Mathematics Journalに受理された. 後期,私は主に空間グラフのFloer homologyを定義しようと努力した.この研究の目的は空間グラフのHeegaard Floer homologyを定義し、そしてその位相的な応用を考えることである.今まで次の結果を得た.GをS^3における連結なbalanced2部空間グラフとし,Gの位相不変量であるHeegaard Floe rhomologyを定義した.更に、Gに新しい辺eを加え,G'=GU{e}が2部空間グラフになることにする.辺εがGのHeegaard Floer homologyにフィルトレーションを一つ誘導することを示し,G'とGのHeegaard Floer homologyの間の関係を一つ発見した.現在この結果に関する論文を執筆中である.これから,一般の空間グラフにもHeegaard Floer homologyを定義してみたいと思う.