Genus (mathematics)
In mathematics, the genus of a topological space such as a surface is an integer representing the maximum number of cuts that can be made through it without rendering it disconnected. This is roughly equivalent to the number of holes in it, or handles on it.For instance:
- A point, line, and a sphere all have genus zero
- A torus has genus one, as does a coffee cup as a solid object (solid torus), a Möbius strip, and the symbol 0.
- The symbols 8 and B have genus two.
- A pretzel has genus three.
In algebraic geometry there is a definition for the genus of any algebraic curve C. When the field of definition for C is the complex numbers, and C has no singular points, then that definition co-incides with the topological definition applied to the Riemann surface of C (its manifold of complex points). The definition of elliptic curve from algebraic geometry is non-singular curve of genus 1.
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enthusiasm of hers for Mr. Austin as an antidote to her sharp suffering.
concerning Seymour Austin, whom, she imagined, possibly she had not
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Miss,' the maid reported. It signified to Cecilia: no one roaming
commenced it, though sorely wounded, with pity for Nevil's
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jealous, nor any right to reproach him. Her task was to climb back to
down.
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hoped to recover them in Italy, and the calm security of a mind
speed to the ridges of the Italian frontier, across France--she simply
landscape, among the images of Art and the names of patient great men who
them. If at night, in her sleep, he was a memory that conducted her
flight released her. France, too, her rival!--the land of France,
gift, did not wound her with a poisoned dart.--'She knew him first: she
renewed Cecilia's lofty-perching youth. Then--I am in Italy! she sighed
over-satisfying to drown the recollection of past anguish, is baneful to
fire over a heath. She could scarcely feel common pleasure in Rome. It
she had flown from: jealous love, and reproachful; and a shame in it
lightnings, passing shadows. She could have believed in sorcery:
notion of being off her feet, in the claws of a fabulous bird. It.
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