We prove that the category of presheaves of simplicial groupoids and the category of presheaves of 2-groupoids have Quillen closed model structures. We also show that the homotopy categories associated to the two categories are equivalent to the homotopy categories of simplicial presheaves and homotopy 2-types, respectively.

A new definition of the homotopy analysis method is given by means of the decomposition method in this paper. The convergence of the homotopy decomposition method is proved under some reasonable hypotheses, which provide the theoretical basis of the homotopy decomposition method for solving nonlinear problems. AMS subject classification: 34A34.

Homotopy And Simple Homotopy Theory The ultimate sales letter will provide you a distinctive book to overcome you life to much greater. Book, as one of the reference to get many sources can be considered as one that will connect the life to the experience to the knowledge. By having book to read, you have tried to connect your life to be better. It will encourage your quality not only for your ...

Proper homotopy groups analogous to the usual homotopy groups are defined. They are used to prove, modulo the Poincare conjecture, that a noncompact 3-manifold having the proper homotopy type of a closed product F x [0, l] or a half-open product F X [O, 1) where F is a 2-manifold is actually homeomorphic to Fx [0, l] or F x [0, 1), respectively. By defining a concept for noncompact manifolds si...

Homotopy Theory: The Interaction of Category Theory and Homotopy theory A revised version of the 2001 article

We define a notion of homotopy in the effective topos. AMS Subject Classification (2000): 18B25 (Topos Theory),55U35 (Abstract and axiomatic homotopy theory)

We construct an analogue of the normaliser decomposition for p–local finite groups (S,F ,L) with respect to collections of F –centric subgroups and collections of elementary abelian subgroups of S . This enables us to describe the classifying space of a p–local finite group, before p–completion, as the homotopy colimit of a diagram of classifying spaces of finite groups whose shape is a poset a...

We establish a general method to produce cofibrant approximations in the model category US(C,D) of S-valued C-indexed diagrams with D-weak equivalences and D-fibrations. We also present explicit examples of such approximations. Here, S is an arbitrary cofibrantly generated simplicial model category and D ⊂ C are small categories. An application to the notion of homotopy colimit is presented.