L-space surgery and twisting operation

Twisting and Turning in Space

ion and classification continues, What's Euclidean On a perfectly flat surface, parallel lines never meet. A triangle drawn on such a plane has interior angles that add up to 1800. A straight line is the shortest distance between two points. These and other postulates and results are part of the geometry first invented by Euclid more than 2,000 years ago. Later mathematicians refined and extend...

Cosmetic surgery in L–space homology spheres

In particular, let K be a framed knot in a closed oriented three-manifold Y . For a rational number r , let Yr .K/ be the manifold obtained by Dehn surgery along K with slope r . Two surgeries along K with distinct slopes r and r 0 are called equivalent if there exists an orientation-preserving homeomorphism of the complement of K taking one slope to the other; and they are called truly cosmeti...

Twisting of Siegel Modular Forms with Characters, and L-functions

Linear twistings of Siegel modular forms with Dirichlet characters are considered. It is shown that the twisting operators transform modular forms to modular forms. Commutation of twisting operators and Hecke operators is examined. It is proved that under certain conditions the spinor zeta-function of a twisted modular form can be interpreted as the L-function of the initial modular form with t...

Graviton: Twisting Space and Time to Speed-up CoFlows

q-EUCLIDEAN SPACE AND QUANTUM GROUP WICK ROTATION BY TWISTING

We study the quantum matrix algebra R21x1x2 = x2x1R and for the standard 2×2 case propose it for the co-ordinates of q-deformed Euclidean space. The algebra in this simplest case is isomorphic to the usual quantum matrices Mq(2) but in a form which is naturally covariant under the Euclidean rotations SUq(2)⊗SUq(2). We also introduce a quantum Wick rotation that twists this system precisely into...