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The Ptolemy variety for SL(2; C) is an invariant of a topological ideal triangulation
of a compact 3-manifold M. It is closely related to Thurston’s gluing equation variety. The
Ptolemy variety maps...
We define Ptolemy coordinates for representations that are not necessarily
boundary-unipotent. This gives rise to a new algorithm for computing the SL(2; C) Apolynomial, and more generally the ...
The Ptolemy coordinates for boundary-unipotent SL(n; C)-representations of a
3-manifold group were introduced in [7] inspired by the A-coordinates on higher Teichmuller
space due to Fock and Goncha...
The Circumference of the Earth and Ptolemy’s World Map
The Circumference the Earth Ptolemy’s World Map
2015/3/26
The interlink between the determination of the circumference of the Earth and the geographical mapping performed by Ptolemy in his Geography (c. 150 AD) is discussed. As Ptolemy himself stated, he use...
Travelling along the Silk Road: A new interpretation of Ptolemy’s coordinates
Travelling along the Silk Road Ptolemy’s coordinates
2015/3/26
Starting from the assumption that Ptolemy worked with a value for the circumference of the Earth that was much too small, his coordinates may be recalculated for the circumference measured by Eratosth...
Ptolemy’s Circumference of the Earth (TOPOI – Towards a Historical Epistemology of Space)
Ancient Geography Ptolemy Eratosthenes
2015/3/26
The relationship between the determination of the circumference of the Earth and the geographical mapping performed by Ptolemy in his Geography is discussed. A simple transformation of the Ptolemaic c...
Moebius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces
Moebius structures Ptolemy spaces boundary at infinity of complex hyperbolic spaces
2011/1/19
The paper initiates a systematic study of M¨obius structures and Ptolemy spaces. We conjecture that every compact Ptolemy space with circles and many space inversions is M¨obius equivalent to the boun...