Homotopy 2-Types of Low Order
نویسندگان
چکیده
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 |, and the order of a quasi-isomorphism class of crossed modules to be the least order of any crossed module in the class. We then define the order of a homotopy 2-type X to be the order of the corresponding quasiisomorphism class of crossed modules. In this paper we describe a computer implementation that inputs a finite crossed module of reasonably small order and returns a quasi-isomorphic crossed module of least order. Underlying the function is a catalogue of all quasi-isomorphism classes of order m ≤ 127,m 6= 32, 64, 81, 96 and a catalogue of all isomorphism classes of crossed modules of order m ≤ 255.
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ورودعنوان ژورنال:
- Experimental Mathematics
دوره 23 شماره
صفحات -
تاریخ انتشار 2014