Page 316 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 316
GRAPHS, POLYNOMIALS, SURFACES, AND KNOTS (MS-49)
A list orientation of graphs
Kenta Ozeki, ozeki-kenta-xr@ynu.ac.jp
Yokohama National University, Japan
For a list L of a graph G with L(v) ⊆ {0, 1, . . . , degG(v)} for each vertex v, an L-orientation
of G is one such that the outdegree of each vertex v is contained in the list L(v). In this talk, we
discuss the existence of an L-orientation. In particular, we apply a polynomial method to plane
graphs to find an L-orientation if the list L satisfies certain conditions.
Partial Twuality Polynomials
Thomas W. Tucker, ttucker@colgate.edu
Colgate University, United States
Poincare duality * and Petrie duality ×, as operators on ribbon graphs (cellular graph embed-
dings), generate a group of operators, or twualities, isomorphic to the symmetric group Σ3. Any
of these twualities T can be restricted to a subset of edges A to give a partial twuality GT|A.
Recent papers with Jonathan Gross and Toufik Mansour introduce the partial-T polynomial of
G, the generating function enumerating partial-T twuals of G by euler genus. Interpretation of
partial twuals in terms of partial permutations in the monodromy of G allows computation of
these polynomials for small examples. Various properties and examples of partial polynomi-
als are discussed with particular attention to interpolating and log-concave behavior, as well as
possible connections to Bollobás-Riordan polynomials.
Ternary self-distributive cohomology and invariants of framed links and
knotted surfaces with boundary
Emanuele Zappala, emanuele.amedeo.zappala@ut.ee
University of Tartu, Estonia
Coauthors: Viktor Abramov, Masahico Saito
In this talk I will describe how to construct certain state-sum invariants of framed links that
utilize the cohomology groups of ternary self-distributive racks and quandles. I will argue that
these invariants can be considered, in an appropriate sense, as quantum invariants and give
examples from Hopf algebras and 3-Lie algebras, such as ternary Nambu-Lie algebras. Finally,
I will explain how these ideas generalize to the case of (compact and oriented) surfaces with
boundary knotted in the 3-space.
314
A list orientation of graphs
Kenta Ozeki, ozeki-kenta-xr@ynu.ac.jp
Yokohama National University, Japan
For a list L of a graph G with L(v) ⊆ {0, 1, . . . , degG(v)} for each vertex v, an L-orientation
of G is one such that the outdegree of each vertex v is contained in the list L(v). In this talk, we
discuss the existence of an L-orientation. In particular, we apply a polynomial method to plane
graphs to find an L-orientation if the list L satisfies certain conditions.
Partial Twuality Polynomials
Thomas W. Tucker, ttucker@colgate.edu
Colgate University, United States
Poincare duality * and Petrie duality ×, as operators on ribbon graphs (cellular graph embed-
dings), generate a group of operators, or twualities, isomorphic to the symmetric group Σ3. Any
of these twualities T can be restricted to a subset of edges A to give a partial twuality GT|A.
Recent papers with Jonathan Gross and Toufik Mansour introduce the partial-T polynomial of
G, the generating function enumerating partial-T twuals of G by euler genus. Interpretation of
partial twuals in terms of partial permutations in the monodromy of G allows computation of
these polynomials for small examples. Various properties and examples of partial polynomi-
als are discussed with particular attention to interpolating and log-concave behavior, as well as
possible connections to Bollobás-Riordan polynomials.
Ternary self-distributive cohomology and invariants of framed links and
knotted surfaces with boundary
Emanuele Zappala, emanuele.amedeo.zappala@ut.ee
University of Tartu, Estonia
Coauthors: Viktor Abramov, Masahico Saito
In this talk I will describe how to construct certain state-sum invariants of framed links that
utilize the cohomology groups of ternary self-distributive racks and quandles. I will argue that
these invariants can be considered, in an appropriate sense, as quantum invariants and give
examples from Hopf algebras and 3-Lie algebras, such as ternary Nambu-Lie algebras. Finally,
I will explain how these ideas generalize to the case of (compact and oriented) surfaces with
boundary knotted in the 3-space.
314
