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Autore principale:	Schuetz, Dirk
Natura:	Preprint
Pubblicazione:	2025
Soggetti:	Geometric Topology 57K18 (Primary) 57K10 (Secondary)
Accesso online:	https://arxiv.org/abs/2504.07806
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author	Schuetz, Dirk
author_facet	Schuetz, Dirk
contents	We use the Mackaay-Vaz universal $sl(3)$-link homology to deepen the study of $s$-invariants on Khovanov's link homology associated to $sl(3)$. Such $s$-invariants have already been studied by Lobb and Wu in characteristic 0 and we show how to extend this to other characteristics, particularly to $p=3$. We also use Bar-Natan's scanning algorithm for efficient calculations of these invariants, and exhibit more examples of unusual behaviour that has been previously observed by Lewark-Lobb.
format	Preprint
id	arxiv_https___arxiv_org_abs_2504_07806
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	On Variations of s-invariants from sl(3)-link homology Schuetz, Dirk Geometric Topology 57K18 (Primary) 57K10 (Secondary) We use the Mackaay-Vaz universal $sl(3)$-link homology to deepen the study of $s$-invariants on Khovanov's link homology associated to $sl(3)$. Such $s$-invariants have already been studied by Lobb and Wu in characteristic 0 and we show how to extend this to other characteristics, particularly to $p=3$. We also use Bar-Natan's scanning algorithm for efficient calculations of these invariants, and exhibit more examples of unusual behaviour that has been previously observed by Lewark-Lobb.
title	On Variations of s-invariants from sl(3)-link homology
topic	Geometric Topology 57K18 (Primary) 57K10 (Secondary)
url	https://arxiv.org/abs/2504.07806

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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