Timeline for Duality between proper homotopy theory and strong shape theory
Current License: CC BY-SA 3.0
4 events
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| Jan 19, 2014 at 6:36 | comment | added | Tim Porter | Damien: the cohomological duality inherent in the Edwards and Hastings more precise version of Chapman's result is the geometric side of the very classical duality theorems of algebraic topology. The algebraic geometry side of things is less immediately `geometric' as it deals with sheaves. Perhaps one way to see things is to think of proper homotopy theory as being about exhausting a space by compact bits, (and so about the Ind-category of spaces), whilst shape is about the Pro-category. These categories also arise in Verdier's derived functors so ... ??? | |
| Dec 13, 2011 at 20:32 | comment | added | DamienC | Many thanks for your answer. I am a total beginner with shape theory (and not really an expert in homotopy theory). I guess the paper of Batanin you refer to is web.science.mq.edu.au/~mbatanin/SHAPE0.dvi I'll have a look at it. Tanks again. | |
| Dec 13, 2011 at 17:13 | history | edited | Tim Porter | CC BY-SA 3.0 |
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| Dec 13, 2011 at 17:08 | history | answered | Tim Porter | CC BY-SA 3.0 |