{"id":16342,"date":"2024-12-12T10:01:48","date_gmt":"2024-12-12T15:01:48","guid":{"rendered":"https:\/\/www.crmath.ca\/page-calendrier\/soutien-datascience\/"},"modified":"2025-06-18T08:21:27","modified_gmt":"2025-06-18T12:21:27","slug":"minicourses-4-manifolds","status":"publish","type":"page-calendrier","link":"https:\/\/www.crmath.ca\/en\/page-calendrier\/minicourses-4-manifolds\/","title":{"rendered":"Mini-courses-4-manifolds"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1420.64px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:0px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-text fusion-text-1\"><p><strong>July 2-4, 2025<\/strong><\/p>\n<p>Invited speakers:<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"font-weight: 400;\">Anthony Conway (UT Austin): Embedding surfaces in 4-manifolds<\/li>\n<li style=\"font-weight: 400;\">James Davis (University of Indiana): Introduction to surgery theory<\/li>\n<li>Mark Powell (University of Glasgow): Classification of topological 4-manifold<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h4><a href=\"https:\/\/www.crmath.ca\/horaire\/2025\/4-Manifolds\/pdf\/Schedule-minicours.pdf\" target=\"_blank\" rel=\"noopener\">Mini-courses schedule<\/a><\/h4>\n<p><strong>Lectures<\/strong>:<br \/>\n<strong><br \/>\nAnthony Conway<\/strong>:<\/p>\n<p>These lectures are concerned with spheres in closed, simply-connected 4-manifolds. Emphasis will be placed on the case where the complement of the sphere has abelian fundamental group, i.e. so-called \u201csimple spheres\u201d.<\/p>\n<p>Lecture 1: Definitions, examples and invariants. The goal is to discuss examples of knotted spheres as well as invariants based on the algebraic topology of the sphere exterior.<\/p>\n<p>Lecture 2: Simple spheres up to isotopy. This lecture describes sufficient conditions for two simple spheres to be isotopic. This will be based on work of Lee-Wilczynski and on joint work with Powell.<\/p>\n<p>Lecture 3: Realisation and enumeration. We conclude by discussing necessary and sufficient conditions for a given second homology class to be realised by a simple sphere. This will be based on work of Lee-Wilczynski and on joint work with Piccirillo and Powell.<\/p>\n<p><strong>James Davis:<br \/>\n<\/strong><\/p>\n<p>Lecture 1:\u00a0 Manifolds<br \/>\nThis will be a whirlwind tour of standard topics in manifold theory including the following topics:\u00a0\u00a0 topological and smooth manifolds (with boundary), the surgery equivalence relation, bordism, handles, Morse theory and handlebody structure on manifolds, Dehn surgery, the Lickorish-Wallace Theorem, and Kirby diagrams for three-manifolds (surgery) and four-manifolds (handlebodies).<\/p>\n<p>Lecture 2: Uniqueness and existence<br \/>\nThis will be \u201csurgery theory.\u201d\u00a0\u00a0 The statement of the uniqueness and existence questions for homotopy structures on manifolds.\u00a0\u00a0\u00a0 The motivating examples of S^4 (the 4d Poincare conjecture), the cone on the Poincare homology sphere, and the E_8 manifolds.\u00a0 Rochlin\u2019s and Donaldson\u2019s theorem.\u00a0 The (stable) h-cobordism theorem.\u00a0\u00a0\u00a0 Degree one normal maps, surgery up to the middle dimension, and the surgery exact sequence.\u00a0\u00a0 L-groups.\u00a0 Good groups.<\/p>\n<p>Lecture 3:\u00a0 Applications and the global structure of surgery<br \/>\nThe first half of the talk will be applying the above theory to see why homology 3-spheres bound contractible manifolds, the 4d topological Poincare conjecture, why Alexander 1 knots (and links?) are topological slice, and the existence of *CP^2.\u00a0\u00a0The second half of the lecture will indicate some of my applications of the algebraic surgery exact sequence to 4-manifolds &#8211; including how characteristic class formulae for surgery obstructions interact with stable diffeomorphisms and how the total surgery obstruction constructs aspherical 4-manifolds with boundary.<\/p>\n<p><strong>Mark Powell:<\/strong><\/p>\n<p>I will explain how to classify 4-manifolds up to homotopy equivalence, and how to upgrade this to a homeomorphism classification using surgery theory. I will focus on the cases of trivial and infinite cyclic fundamental group for simplicity, while describing a framework that can be applied for more general fundamental groups. Here is the plan for the lectures.<\/p>\n<p>Lecture 1: Homotopy classifications.<\/p>\n<p>Lecture 2: Homotopy automorphisms.<\/p>\n<p>Lecture 3: Homeomorphism classifications<\/p>\n<h4><strong>\u00a0<\/strong><\/h4>\n<p><!--more--><\/p>\n<\/div><\/div><\/div><\/div><\/div>\n","protected":false},"author":14,"template":"","class_list":["post-16342","page-calendrier","type-page-calendrier","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/page-calendrier\/16342","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/page-calendrier"}],"about":[{"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/types\/page-calendrier"}],"author":[{"embeddable":true,"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":17,"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/page-calendrier\/16342\/revisions"}],"predecessor-version":[{"id":18176,"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/page-calendrier\/16342\/revisions\/18176"}],"wp:attachment":[{"href":"https:\/\/www.crmath.ca\/en\/wp-json\/wp\/v2\/media?parent=16342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}