By Angeliki E. Laiou
The stories during this quantity replicate the author's curiosity in heritage because it was once lived: not just social and monetary constructions, however the women and men, jointly and separately, who made them functionality. The function of ladies in Byzantine economic system and society is located to be even more vital than were believed; their participation in exchange and production is verified, as is the position of aristrocratic girls within the fiscal affairs of the family; the query of girl literacy can be mentioned. stories at the Byzantine relations, established largely at the felony providers, research the formation of matrimonial ties in addition to the perform of divorce and concubinage within the thirteenth century. the second one a part of the quantity is targeted at the economic system of alternate in Byzantium among 1204 and the autumn of the Empire. Byzantine alternate and production are position within the context of the industrial advancements of the japanese Mediterranean, with the belief that, while the actions of Byzantine and Greek retailers have been even more enormous than students had inspiration, they have been subordinated to the desires of the Italian-dominated exchange process, whereas Byzantine production declined.
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Additional info for Gender, Society, and Economic Life in Byzantium (Variorum Reprints)
Example text
The starting point is the case of nonseparating simple closed curves, and the inductive step is Example 5: cutting along the first few arcs, the next arc becomes a nonseparating arc on the cut surface. Note that Example 1 is the case k = 2. One can also prove by induction that every chain in Sg of even length is nonseparating, and so such chains must be topologically equivalent. We remark that the homeomorphism representing the change of coordinates in each of the six examples above can be taken to be orientation preserving.
The way we will compute Mod(S0,3 ) is to understand its action on some fixed arc in S0,3 . The surface obtained by cutting S0,3 along this arc is a punctured disk, and so we will be able to apply the Alexander lemma. This is in general how we use the cutting procedure for surfaces in order to perform inductive arguments. In this section it will be convenient to think of S0,3 as a sphere with three marked points (instead of three punctures). In order to determine Mod(S0,3 ) we first need to understand simple proper arcs in S0,3 .
44 CHAPTER 1 In fact a stronger, relative result holds: if two homeomorphisms are homotopic relative to ∂S then they are isotopic relative to ∂S. 8. 12 also holds when S has finitely many marked points. In that case, we need to expand our list of counterexamples to include a sphere with one or two marked points. 2 H OMEOMORPHISMS VERSUS DIFFEOMORPHISMS It is sometimes convenient to work with homeomorphisms and sometimes convenient to work with diffeomorphisms. For example it is easier to construct the former but we can apply differential topology to the latter.