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Amer. Math. Soc. <strong>377</strong> (2024), 2897-2923 </dd> <dd> DOI: https://doi.org/10.1090/tran/9104 </dd> <dd> Published electronically: February 13, 2024 </dd> <dd class="mathviewerPDFLink"> <a href = "viewer"><strong>HTML</strong></a> | <a href="S0002-9947-2024-09104-3.pdf"><small>PDF</small></a> | <a href="https://www.copyright.com/openurl.do?issn=1088-6850&WT.mc.it=American%20Mathematical%20Society" target="_blank">Request permission</a> </dd> </dl> </header> <section id="Abstract"> <h2>Abstract:</h2> <p>In this paper, we construct a compactification of the space of Bridgeland stability conditions on a smooth projective curve, as an analogue of Thurston compactifications in Teichmüller theory.</p> <p>In the case of elliptic curves, we compare our results with the classical one of the torus via homological mirror symmetry and give the Nielsen–Thurston classification of autoequivalences using the compactification.</p> <p>Furthermore, we observe an interesting phenomenon in the case of the projective line.</p> </section> <section id="references"> <details> <summary>References</summary> <ul><li><a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Bapat%2C%20Asilata">Asilata Bapat</a>, <a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Becker%2C%20Louis">Louis Becker</a>, and <a href="https://mathscinet.ams.org/mathscinet/search/authors.html?authorName=Licata%2C%20Anthony%20M.">Anthony M. 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Amer. Math. Soc. <strong>377</strong> (2024), 2897-2923 </li> <li>MSC (2020): Primary 14J33, 18G80, 57K20 <li>DOI: https://doi.org/10.1090/tran/9104</li> <li>MathSciNet review: <a href = "https://mathscinet.ams.org/mathscinet-getitem?mr=4744772">4744772</a></li> </ul> </details> </section> </article> </section> </article> </section> </main> </div>   <hr class="mx-auto"> <footer id="pagefooter" class="text-center"> <div class="container text-center"> <div class="row">  <div class="col-12 mb-1"> <p> American Mathematical Society · <a href="https://goo.gl/maps/ZvJdkQEC79p" title="Google map 201 Charles Street Providence, Rhode Island" aria-label="Google map to AMS headquarters"> 201 Charles Street Providence, Rhode Island 02904-2213 </a> · <a href="/reach" aria-label="Contact Us">Contact Us</a> </p> </div>  <script src="https://kit.fontawesome.com/2ad6d7fbd6.js" crossorigin="anonymous" defer></script>  <nav class="col-12 mb-1" aria-label="Social media links"> <ul class="list-inline"> <li class="list-inline-item"> <a href="https://www.facebook.com/amermathsoc" class="link-dark" title="Follow us on Facebook" aria-label="View the AMS on Facebook"> <i class="fa-brands fa-facebook-f" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://bsky.app/profile/amermathsoc.bsky.social" class="link-dark" title="Follow us on Bluesky" aria-label="View the AMS on Bluesky"> <i class="fa-brands fa-bluesky"></i></a></li> <li class="list-inline-item"> <a href="https://twitter.com/amermathsoc" class="link-dark" title="Follow us on X" aria-label="View the AMS on X"> <i class="fa-brands fa-x-twitter" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://www.linkedin.com/company/51001" class="link-dark" title="Follow us on LinkedIn" aria-label="View the AMS on LinkedIn"> <i class="fa-brands fa-linkedin-in" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://www.instagram.com/amermathsoc" class="link-dark" title="Follow us on Instagram" aria-label="View the AMS on Instagram"> <i class="fa-brands fa-instagram" aria-hidden="true"></i></a></li> <li class="list-inline-item"> <a href="https://www.youtube.com/amermathsoc" class="link-dark" title="Follow us on YouTube" aria-label="View the AMS on YouTube"> <i class="fa-brands fa-youtube" aria-hidden="true"></i></a></li> </ul> </nav>  <div class="col-12"> <p><small> © <a href="/copyright" aria-label="Copyright policy">Copyright</a> <span id="copyYear">2024</span> American Mathematical Society · <a href="/privacy" aria-label="Privacy statement">View Our Privacy Statement</a> · <a href="/tou" aria-label="Terms of use">Terms of Use</a> · <a href="/accessibility" aria-label="Accessibility policy">Accessibility and AMS Online Content</a> </small></p> <p><small> AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and service marks of the American Mathematical Society and registered in the U.S. Patent and Trademark Office. </small></p> </div> </div> </div> <script> // Dynamically update the copyright year document.getElementById('copyYear').textContent = new Date().getFullYear(); </script> </footer>