CINXE.COM

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href="https://blogs.mat.ucm.es/angelgonzalezprieto/seminars/">Seminars<svg class="icon icon-angle-down" aria-hidden="true" role="img"> <use href="#icon-angle-down" xlink:href="#icon-angle-down"></use> </svg></a> <ul class="sub-menu"> <li id="menu-item-35" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-35"><a href="https://blogs.mat.ucm.es/angelgonzalezprieto/maphyag-seminar/">MAPHYAG Seminar</a></li> </ul> </li> <li id="menu-item-256" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-256"><a href="https://jovenes2025.rsme.es/">Congreso J贸venes RSME 2025</a></li> </ul></div> </nav> </div> </div> </header> <div class="site-content-contain"> <div id="content" class="site-content"> <div class="wrap"> <div id="primary" class="content-area"> <main id="main" class="site-main" role="main"> <article id="post-19" class="post-19 page type-page status-publish hentry"> <header class="entry-header"> <h1 class="entry-title">Book</h1> </header> <div class="entry-content"> <h2>Geometry and Topology of Manifolds</h2> <h3>Surfaces and Beyond</h3> <p>Jointly with Vicente Mu帽oz and Juan 脕ngel Rojo, we have published the monograph <a class="a_white" href="https://bookstore.ams.org/gsm-208/?_zs=WHBcC1&_zl=3DKs5" target="new"><em>Geometry and Topology of Manifolds: Surfaces and Beyond</em></a>, as part of the collection Graduate Studies in Mathematics of the American Mathematical Society</p> <p>The textbook is oriented to Master’s students and PhD students, with a view towards the interplay between different types of geometric structures on manifolds (topological, differentiable, Riemannian, complex, algebraic, etc.), with special attention to the case of surfaces.</p> <p>The book can be used as basic bibliography for advanced graduate courses, as it has been done in the Master’s degree in Mathematics at Universidad Complutense de Madrid. Nevertheless, the textbook also contains cornerstone results that may be independently used for courses on differential topology or algebraic topology, like the classification of compact surface, the degree-genus formula, homology and cohomology in various versions, the Gauss-Bonnet theorem or a thorough study of manifolds of constant sectional curvature, among others. Moreover, it also includes a novel proof of the uniformization theorem through the curvature flow and orbifolds.</p> <p><a class="a_white" href="https://bookstore.ams.org/gsm-208/?_zs=WHBcC1&_zl=3DKs5" target="new"><em>Geometry and Topology of Manifolds: Surfaces and Beyond.</em></a><br /> Graduate Studies in Mathematics (American Mathematical Society). ISBN: 978-1-4704-6132-4</p> <p><a href="https://bookstore.ams.org/gsm-208/?_zs=WHBcC1&_zl=3DKs5"><img class="alignnone size-medium wp-image-20" src="http://blogs.mat.ucm.es/angelgonzalezprieto/wp-content/uploads/sites/89/2023/05/AMSBookCover-210x300.png" alt="" width="210" height="300" srcset="https://blogs.mat.ucm.es/angelgonzalezprieto/wp-content/uploads/sites/89/2023/05/AMSBookCover-210x300.png 210w, https://blogs.mat.ucm.es/angelgonzalezprieto/wp-content/uploads/sites/89/2023/05/AMSBookCover-717x1024.png 717w, https://blogs.mat.ucm.es/angelgonzalezprieto/wp-content/uploads/sites/89/2023/05/AMSBookCover.png 756w" sizes="(max-width: 210px) 100vw, 210px" /></a></p> <h2><strong>Table of contents</strong></h2> <ol> <li>Topological surfaces <ul> <li>Topological and smooth manifolds</li> <li>PL structures</li> <li>Planar representations of surfaces</li> <li>Orientability</li> <li>Classification of compact surfaces</li> </ul> </li> <li>Algebraic topology <ul> <li>Homotopy theory</li> <li>Covers</li> <li>Singular homology</li> <li>Simplicial homology</li> <li>De Rham cohomology</li> <li>Poincar茅 duality</li> </ul> </li> <li>Riemannian geometry <ul> <li>Riemannian metrics. Curvature. Geodesics</li> <li>Riemannian surfaces and the Gauss-Bonnet theorem</li> <li>Isotropic, symmetric, and homogeneous manifolds</li> </ul> </li> <li>Constant curvature <ul> <li>Positive constant curvature</li> <li>Vanishing constant curvature</li> <li>Negative constant curvature</li> <li>Classical geometries</li> </ul> </li> <li>聽Complex geometry <ul> <li>Complex manifolds</li> <li>K盲hler manifolds</li> <li>Complex curves</li> <li>Classification of complex curves</li> <li>Elliptic curves</li> </ul> </li> <li>聽Global analysis <ul> <li>Conformal structures</li> <li>Hodge theory</li> <li>Metrics of constant curvature</li> <li>The curvature flow</li> </ul> </li> </ol> </div> </article> </main> </div> </div> </div> <footer id="colophon" class="site-footer" role="contentinfo"> <div class="wrap"> <div class="site-info"> <a href="https://es.wordpress.org/" class="imprint"> Funciona gracias a WordPress </a> </div> </div> </footer> </div> </div> <aside id="moove_gdpr_cookie_info_bar" class="moove-gdpr-info-bar-hidden moove-gdpr-align-center moove-gdpr-dark-scheme gdpr_infobar_postion_bottom" role="note" aria-label="Banner de cookies RGPD"> <div class="moove-gdpr-info-bar-container"> <div class="moove-gdpr-info-bar-content"> <div class="moove-gdpr-cookie-notice"> <p>Esta web utiliza cookies para ofrecerte la mejor experiencia de navegaci贸n posible.</p><p>Descubre m谩s o ajusta tus <span data-href="#moove_gdpr_cookie_modal" class="change-settings-button">ajustes</span>.</p></div>  <div class="moove-gdpr-button-holder"> <button class="mgbutton moove-gdpr-infobar-allow-all">Aceptar</button> </div>  </div>  </div>  </aside>  <script type='text/javascript'> /* <![CDATA[ */ var wpcf7 = {"apiSettings":{"root":"https:\/\/blogs.mat.ucm.es\/angelgonzalezprieto\/wp-json\/contact-form-7\/v1","namespace":"contact-form-7\/v1"}}; 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