Related papers: Geometric Methods In Heegaard Theory
We use a new geometric construction, grope splitting, to give a sharp bound for separation of surfaces in 4-manifolds. We also describe applications of this technique in link-homotopy theory, and to the problem of locating pi_1-null…
We review the {\it Noether Symmetry Approach} as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact…
We give an overview of some recent results in hypersymplectic and para-quaternionic Kahler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of…
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…
A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of…
We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.
We discuss geometric properties of covers of closed hyperbolic manifolds of dimension $n\geq 3$, branched along a totally geodesic codimension two submanifold $\Sigma$. The results are mostly known to the experts but hard to find in the…
By combining tools from different areas of mathematics, we obtain 3D visualizations of elliptic curves over different fields that faithfully capture the underlying algebra and geometry.
We compute the Heegaard Floer homology of an oriented 3-manifold obtained by a negative rational surgery along an arbitrary algebraic knot.
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…
We study the geometry of a class of $n$-dimensional smooth projective varieties constructed by Schreieder for their noteworthy Hodge-theoretic properties. In particular, we realize Schreieder's surfaces as elliptic modular surfaces and…
The study of triangulations on manifolds is closely related to understanding the three-dimensional homology cobordism group. We review here what is known about this group, with an emphasis on the local equivalence methods coming from…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the…
In this paper, we give an algorithm to build all compact orientable atoroidal Haken 3-manifolds with tori boundary or closed orientable Haken 3-manifolds, so that in both cases, there are embedded closed orientable separating incompressible…
We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is bounded below by the smaller of twice its genus or half its Hempel distance. This is a…
In this note we give a p-adic proof of Hodge symmetry for smooth, projective threefolds over complex numbers.
This paper has been withdrawn by the author, as the proof of Theorem 3.2 contains a flaw; subsequently, both it and Theorem 3.3 are not known to hold. The content of Section 5 has been improved and expanded upon in two separate papers. The…
In this survey article, we discuss some recent progress on geometric analysis on manifold with ends. In the final section, we construct manifolds with ends with oscillating volume functions which may turn out to have a different heat kernel…