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Algebraic models of disconnected equivariant spaces. Second edition (completed and revised)
Autor: Marek Golasiński
Cena: 18 PLN
ISBN: 8323115303
Wydawca: Uniwersytetu Mikołaja Kopernika
Wydawca: 156 stron, oprawa miękka, format 170x240
The homotopy groups of an arbitrary space are "fearsome beasties" to compute. In the early 1950's, Serre introduced the idea of doing homotopy theory modulo a class of groups. A more recent approach developed by Quillen in his fundamental paper involves rational spaces, i.e., spaces whose homotopy groups are rational vector spaces. Rational homotopy theory attempts to tame these beasts by making the calculation effectively computable. It is the study of the rational homotopy category, that is, the category obtained from the category of simply connected spaces by localizing with respect to the family of those maps which are isomorphisms modulo the class (in the sense of Serre) of torsion abelian groups. Quillen made these ideas precise and proved that homotopy categories of certain relatively simple algebraic categories are equivalent to the rational homotopy category of simply connected spaces. Sullivan introduced the rational de Rham theory for connected simplicial complexes and applied it to show that the de Rham algebra AX of Q-differential forms on a simply connected complex X of finite type determines its rational homotopy type.