We describe a class of topological field theories called “balanced topological field theories.” These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of “iterated superspaces” that carry two differentials. We find the ...

Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological Phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented ...

We define the topological entropy per unit volume in parabolic PDE’s such as the complex GinzburgLandau equation, and show that it exists and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows ...

The literature contains several extensions of the standard definitions of topological entropy for a continuous self-map f : X→X from the case when X is a compact metric space to the case when X is allowed to be noncompact. These extensions all require the space X to be totally bounded, or equivalently to have a compact completion, and are invariants of uniform conjugacy. When themap f is unifor...

We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allow...

We suggest a mechanism whereby the three generations of quarks and leptons correspond to surface modes in a five-dimensional theory. These modes arise from a nonlinear fermion dispersion relation in the extra dimension, much in the same manner as fermion surface modes in a topological insulator or lattice implementation of domain wall fermions. We also show that the topological properties can p...

Symmetry-protected topological (SPT) phases are bulk-gapped quantum phases with symmetries, which have gapless or degenerate boundary states as long as the symmetries are not broken. The SPT phases in free fermion systems, such as topological insulators, can be classified; however, it is not known what SPT phases exist in general interacting systems. We present a systematic way to construct SPT...

This paper will be a brief introduction to various groups of matrices and their algebraic, analytic, and topological properties. We consider curves in matrix groups and use them to define the dimension of a matrix group as an important invariant. We then define the matrix exponential and use it to further investigate curves in matrix groups, and to prove our main topological result that every m...

Static topologically-nontrivial configurations in sigma-models, for spatial dimension D ≥ 2, are unstable. The question addressed here is whether such sigma-model solitons can be stabilized by steady rotation in internal space; that is, rotation in a global SO(2) symmetry. This is the mechanism which stabilizes Q-balls (non-topological solitons). The conclusion is that the Q-mechanism can stabi...

S OF SHORT COMMUNICATIONS AND POSTERS Alonso González, Clementa Title: Topological invariants of singularities of real vector fields in dimension three. Abstract: We give topological invariants for a wide class H(π) of absolutely isolated singularities of three-dimensional vector fields. Our invariants are complete once the desingularization morphism π is fixed. They are obtained in terms of a ...