32 research outputs found
Generalized characteristic polynomials of graph bundles
In this paper, we find computational formulae for generalized characteristic
polynomials of graph bundles. We show that the number of spanning trees in a
graph is the partial derivative (at (0,1)) of the generalized characteristic
polynomial of the graph. Since the reciprocal of the Bartholdi zeta function of
a graph can be derived from the generalized characteristic polynomial of a
graph, consequently, the Bartholdi zeta function of a graph bundle can be
computed by using our computational formulae
Monotone Lagrangians in flag varieties
In this paper, we give a formula for the Maslov index of a gradient
holomorphic disc, which is a relative version of the Chern number formula of a
gradient holomorphic sphere for a Hamiltonian -action. Using the formula,
we classify all monotone Lagrangian non-toric fibers of Gelfand-Cetlin systems
on partial flag manifolds.Comment: 33pages, 20 figures. To appear in IMR
On algebraic structures of the Hochschild complex
We first review various known algebraic structures on the Hochschild
(co)homology of a differential graded algebras under weak Poincar{\'e} duality
hypothesis, such as Calabi-Yau algebras, derived Poincar{\'e} duality algebras
and closed Frobenius algebras. This includes a BV-algebra structure on
or , which in the latter case is an extension of
the natural Gerstenhaber structure on . As an example, after proving
that the chain complex of the Moore loop space of a manifold is a
CY-algebra and using Burghelea-Fiedorowicz-Goodwillie theorem we obtain a
BV-structure on the homology of the free space. In Sections 6 we prove that
these BV/coBVstructures can be indeed defined for the Hochschild homology of a
symmetric open Frobenius DG-algebras. In particular we prove that the
Hochschild homology and cohomology of a symmetric open Frobenius algebra is a
BV and coBV-algebra. In Section 7 we exhibit a BV structure on the shifted
relative Hochschild homology of a symmetric commutative Frobenius algebra. The
existence of a BV-structure on the relative Hochschild homology was expected in
the light of Chas-Sullivan and Goresky-Hingston results for free loop spaces.
In Section 8 we present an action of Sullivan diagrams on the Hochschild
(co)chain complex of a closed Frobenius DG-algebra. This recovers
Tradler-Zeinalian \cite{TZ} result for closed Froebenius algebras using the
isomorphism .Comment: This is the final version. Many improvements and corrections have
been made.To appear in Free Loop Spaces in Geometry and Topology, IRMA
Lectures in Mathematicsand Theoretical Physics, to be published by EMS-P
Recommended from our members
Model Theory and Groups
The aim of the workshop was to discuss the connections between model theory and group theory. Main topics have been the interaction between geometric group theory and model theory, the study of the asymptotic behaviour of geometric properties on groups, and the model theoretic investigations of groups of finite Morley rank around the Cherlin-Zilber Conjecture
Graphs determined by their generalized characteristic polynomials
AbstractFor a given graph G with (0,1)-adjacency matrix AG, the generalized characteristic polynomial of G is defined to be ϕG=ϕG(λ,t)=det(λI-(AG-tDG)), where I is the identity matrix and DG is the diagonal degree matrix of G. In this paper, we are mainly concerned with the problem of characterizing a given graph G by its generalized characteristic polynomial ϕG. We show that graphs with the same generalized characteristic polynomials have the same degree sequence, based on which, a unified approach is proposed to show that some families of graphs are characterized by ϕG. We also provide a method for constructing graphs with the same generalized characteristic polynomial, by using GM-switching
Recommended from our members
On tautological classes of fibre bundles and self-embedding calculus
In this thesis we study the ring of characteristic classes of smooth fibre bundles with a particular focus on tautological classes and the ring that they generate. In the first part we use tools from rational homotopy theory to compute analogues of tautological rings over fibrations, which provides upper bounds on the tautological rings of fibre bundles. In some cases we find an upper bound on the Krull dimension that is sharp.
In the second part, we study the classifying space using the calculus of embeddings which provides a homotopy theoretic approximation. We construct cohomology classes on the self-embedding tower which extend certain characteristic classes that were introduced by Kontsevich. This construction is based on introducing configuration space integrals over the tower itself, which also has some consequences for tautological classes that we explore.Cambridge Trust and King's College Martin Thackeray Scholarshi
Toric topology
We survey some results on toric topology.Comment: English translation of the Japanese article which appeared in
"Sugaku" vol. 62 (2010), 386-41
Toric Topology
Toric topology emerged in the end of the 1990s on the borders of equivariant
topology, algebraic and symplectic geometry, combinatorics and commutative
algebra. It has quickly grown up into a very active area with many
interdisciplinary links and applications, and continues to attract experts from
different fields.
The key players in toric topology are moment-angle manifolds, a family of
manifolds with torus actions defined in combinatorial terms. Their construction
links to combinatorial geometry and algebraic geometry of toric varieties via
the related notion of a quasitoric manifold. Discovery of remarkable geometric
structures on moment-angle manifolds led to seminal connections with the
classical and modern areas of symplectic, Lagrangian and non-Kaehler complex
geometry. A related categorical construction of moment-angle complexes and
their generalisations, polyhedral products, provides a universal framework for
many fundamental constructions of homotopical topology. The study of polyhedral
products is now evolving into a separate area of homotopy theory, with strong
links to other areas of toric topology. A new perspective on torus action has
also contributed to the development of classical areas of algebraic topology,
such as complex cobordism.
The book contains lots of open problems and is addressed to experts
interested in new ideas linking all the subjects involved, as well as to
graduate students and young researchers ready to enter into a beautiful new
area.Comment: Preliminary version. Contains 9 chapters, 5 appendices, bibliography,
index. 495 pages. Comments and suggestions are very welcom
Recommended from our members
Cohomological Aspects of Hamiltonian Group Actions and Toric Varieties
[no abstract available