As a point of departure it is suggested that Quantum Cosmology is a topo-logical concept independent from metrical constraints. Methods of continuous topological evolution and topological thermodynamics are used to construct a cosmological model of the present universe, using the techniques based upon Car-tan's theory of exterior differential systems. Thermodynamic domains, which are either Ope...

Topological quantum computation (TQC) is one of the most promising approaches to quantum computation. The coding of logical qubits to the entanglement of topological quantum numbers promises to solve the de-coherence problem whereas the S-matrices of topological field theories (modular functors) providing unitary representations for braids provide a realization of quantum computer programs with...

Some Cosmological models propose that elementary particles were created during the cooldown of the universe after the “Big Bang”, through a series of symmetry breaking phase transitions[1]. According to these models, these elementary particles are “topological defects” of the cold, ordered phase in which the universe is found today. The equations describing these phase transition of the univers...

What is the shape of space is a long-standing question in cosmology. I review recent advances in cosmic topology since it has entered a new era of experimental tests. High redshift surveys of astronomical sources and accurate maps of the Cosmic Microwave Background radiation (CMB) are beginning to hint at the shape of the universe, or at least to limit the wide range of possibilities. Among tho...

Topological defects are common in many everyday systems. In general, they appear if a symmetry is broken at a rapid phase transition. In this article, I explain why it is believed that they should have also been formed in the early universe and how that would have happened. If topological defects are found, this will provide a way to study observationally the first fractions of a second after t...

Many particle physics models of matter admit solutions corresponding to stable or long-lived topological defects. In the context of standard cosmology it is then unavoidable that such defects will form during phase transitions in the very early Universe. Certain types of defects lead to disastrous consequences for cosmology, others may play a useful role, as possible seeds for the formation of ...

We introduce the category IVRel(H) consisting of interval-valued H-fuzzy relational spaces and relation preserving mappings between them and we study structures of the category IVRel(H) in the viewpoint of the topological universe introduced by Nel. Thus we show that IVRel(H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IVRel(H) is C...

Features of homologous relationship of proteins can provide us a general picture of protein universe, assist protein design and analysis, and further our comprehension of the evolution of organisms. Here we carried out a study of the evolution of protein molecules by investigating homologous relationships among residue segments. The motive was to identify detailed topological features of homolo...

X iv :g rqc /0 31 01 36 v1 3 1 O ct 2 00 3 Non commutative quantum spacetime with topological vortex states, and dark matter in the Universe Ajay Patwardhan Physics Department, St. Xavier’s college, Mahapalika Marg, Mumbai, 400001, India Abstract Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matte...