On Finite Induced Crossed Modules, and the Homotopy 2-type of Mapping Cones Dedicated to the Memory Of
نویسندگان
چکیده
Results on the niteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some nite crossed modules are given, using crossed complex methods.
منابع مشابه
On Finite Induced Crossed Modules, and the Homotopy 2-type of Mapping Cones
Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some finite crossed modules are given, using crossed complex methods.
متن کاملM ar 1 99 5 On finite induced crossed modules , and the homotopy 2 - type of mapping cones
Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some finite crossed modules are given, using crossed complex methods.
متن کاملOn Finite Induced Crossed Modules , and the Homotopy 2 - Type of Mapping
Results on the niteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some nite crossed modules are given, using crossed complex methods.
متن کاملON FINITE INDUCED CROSSED MODULES AND THE HOMOTOPY TYPE OF MAPPING CONES Dedicated to the memory of J
Results on the niteness of induced crossed modules are proved both algebraically and topologically Using the Van Kampen type theorem for the fundamen tal crossed module applications are given to the types of mapping cones of classifying spaces of groups Calculations of the cohomology classes of some nite crossed modules are given using crossed complex methods Introduction Crossed modules were i...
متن کاملHomotopy 2-Types of Low Order
There is a well-known equivalence between the homotopy types of connected CW-spaces X with πnX=0 for n 6= 1, 2 and the quasi-isomorphism classes of crossed modules ∂ : M → P [16]. When the homotopy groups π1X and π2X are finite one can represent the homotopy type of X by a crossed module in which M and P are finite groups. We define the order of such a crossed module to be |∂| = |M | × |P |, an...
متن کامل