The topology of critical processes, Part IV

The topology of critical processes, Part IV

[Marco Grandis]

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The fourth and last paper in my series on ’The topology of critical processes’ is published, in Cahiers (as the previous parts):

The topology of critical processes, IV (The homotopy structure)
M. Grandis

Abstract, Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover 'critical processes', indecomposable and un-stoppable - from the change of state in a memory cell to the action of a thermostat.
The previous parts of this series introduced controlled spaces, examining how they can model critical processes in various domains, and studied their fundamental category. Here we deal with their formal homotopy theory.

Cah. Topol. Géom. Différ. Catég. 66 (2025), no. 2, 46-93.
https://cahierstgdc.com/index.php/volume-lxvi-2025/<https://url.au.m.mimecastprotect.com/s/WCMLCMwGj8Cqj1GNmFJi5c84j-E?domain=cahierstgdc.com>

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Part I: The topology of critical processes, I (Processes and Models)
Cah. Topol. Géom. Différ. Catég. 65 (2024), no. 1, 3–34.
https://cahierstgdc.com/index.php/volume-lxv-2024/<https://url.au.m.mimecastprotect.com/s/K7HKCNLJxki0o814yiRsPcyhMIM?domain=cahierstgdc.com>

Part II: The topology of critical processes, II (The fundamental category)
Cah. Topol. Géom. Différ. Catég. 65 (2024), no. 4, 438–483.
https://cahierstgdc.com/index.php/volume-lxv-2024/<https://url.au.m.mimecastprotect.com/s/K7HKCNLJxki0o814yiRsPcyhMIM?domain=cahierstgdc.com/>

Part III: The topology of critical processes, III (Computing homotopy)
Cah. Topol. Géom. Différ. Catég. 66 (2025), no. 1, 3–18.
https://cahierstgdc.com/index.php/volume-lxvi-2025/<https://url.au.m.mimecastprotect.com/s/WCMLCMwGj8Cqj1GNmFJi5c84j-E?domain=cahierstgdc.com/>


Marco Grandis
e-mail: grandismrc@gmail.com




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