Topology of Finite Graphs.
Topology of plane sections of periodic polyhedra with an application to the truncated octahedron.
Topology of quantizable dynamical systems and the algebra of observables
Topology of the complement of real hyperplanes in CN.
Topology of vortices
Toric structures on near-symplectic 4-manifolds
A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on the base of...
Toroidal decompositions of and a family of 3-dimensional ANR’s (AR’s)
Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups.
Torsion in equivariant cohomology.
Torsion in graph homology
Khovanov homology for knots has generated a flurry of activity in the topology community. This paper studies the Khovanov type cohomology for graphs with a special attention to torsion. When the underlying algebra is ℤ[x]/(x²), we determine precisely those graphs whose cohomology contains torsion. For a large class of algebras, we show that torsion often occurs. Our investigation of torsion led to other related general results. Our computation could potentially be used to predict the Khovanov-Rozansky...
Torsion in Khovanov homology of semi-adequate links
The goal of this paper is to address A. Shumakovitch's conjecture about the existence of ℤ₂-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs, which provides a link between link homology and the well-developed theory of Hochschild homology. In particular, we obtain explicit formulae for torsion and prove that Khovanov homology of semi-adequate links contains ℤ₂-torsion if the corresponding Tait-type graph has a cycle...
Torsion in one-term distributive homology
The one-term distributive homology was introduced in [Prz] as an atomic replacement of rack and quandle homology, which was first introduced and developed by Fenn-Rourke-Sanderson [FRS] and Carter-Kamada-Saito [CKS]. This homology was initially suspected to be torsion-free [Prz], but we show in this paper that the one-term homology of a finite spindle may have torsion. We carefully analyze spindles of block decomposition of type (n,1) and introduce various techniques to compute their homology precisely....
Torsion of Khovanov homology
Khovanov homology is a recently introduced invariant of oriented links in ℝ³. It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic of Khovanov homology is a version of the Jones polynomial for links. In this paper we study torsion of Khovanov homology. Based on our calculations, we formulate several conjectures about the torsion and prove weaker versions of the first two of them. In particular, we prove that all non-split alternating links have their integer Khovanov...
Torsion, TQFT, and Seiberg-Witten invariants of 3-manifolds.
Torus actions on compact quotients.
Torus Actions on Homotopy Complex Projective Spaces.
Torus knots and Dunwoody manifolds.
Torus knots extremizing the Möbius energy.
Torus knots that cannot be untied by twisting.
We give a necessary condition for a torus knot to be untied by a single twisting. By using this result, we give infinitely many torus knots that cannot be untied by a single twisting.
Total cofibres of diagrams of spectra.