BAO Yuanyuan

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Assistant Professor
Field Low dimensional topology, knot theory
Research interests
Heegaard Floer homology, quantum invariants, spatial graph
Current research
Heegaard Floer homology is a topological invariant defined for a 3-manifold or a knot embedded in the 3-sphere. My recent research aims to understand the quantum topological meaning of this invariant. It is well-known that the trivalent spatial graphs take on a big role in the construction of various quantum invariants for a 3-manifold or a knot. So far, I have studied the Heegaard Floer homology for a trivalent graph, the Euler characteristic of this homology (with my collaborator), and its relation with the gl(1|1)-quantum invariant. In the future study, I want to continue this research topic. Figuring out a few problems we met so far about the gl(1|1)-quantum invariant, MOY calculus, and so on will be the next step of my research. I am also interested in the topological properties of spatial graphs.
Selected publications
  1. Y. Bao and Z. Wu, An Alexander polynomial for MOY graphs, Selecta Math. (N. S) 26, 2020.
  2. Y. Bao, A topological interpretation of Viro's gl(1|1)-Alexander polynomial of a graph, Topology and Its Applications, Vol. 267, 106870, 25, 2019.
  3. Y. Bao, Polynomial splittings of Ozsváth and Szabó's d-invariant, Topology Proceedings, Vol. 46, pp. 309-322, 2015.
  4. Y. Bao, On knots having zero negative unknotting number, Indiana Univ. Math. J. 63 No. 2, pp. 597-613, 2014.
  5. Y. Bao, A note on knots with H(2)-unknotting number one, Osaka Journal of Mathematics, Vol. 51, No. 3, pp. 585-596, 2014.
  6. Y. Bao, H(2)-unknotting operation related to 2-bridge links, Topology and Its Applications, Vol. 159, pp. 2158-2167, 2012.
Memberships, awards and activities

The Mathematical Society of Japan