{"id":3232,"date":"2023-09-13T01:05:34","date_gmt":"2023-09-13T08:05:34","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=3232"},"modified":"2023-09-13T01:05:34","modified_gmt":"2023-09-13T08:05:34","slug":"on-the-non-orientable-4-genus-of-double-twist-knots-part-ii-lower-bounds-jim-hoste-pitzer-college","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/on-the-non-orientable-4-genus-of-double-twist-knots-part-ii-lower-bounds-jim-hoste-pitzer-college\/","title":{"rendered":"On the Non-Orientable 4-Genus of Double Twist Knots, Part II: Lower Bounds (Jim Hoste, Pitzer College)"},"content":{"rendered":"<p>The non-orientable 4-genus of a knot K is the smallest first Betti number of any non-orientable surface in the 4-ball spanning the knot. It is defined to be zero if the knot is slice. In joint work with Patrick Shanahan and Cornelia Van Cott, we attempt to determine the value of this invariant for double twist knots. In an earlier talk at this seminar, I presented methods of determining upper bounds by explicitly describing non-orientable spanning surfaces. In this talk I describe methods for establishing lower bounds using linking forms on 4-manifolds and a major result of Donaldson. These methods suffice to compute the non-oprientable 4-genus of several infinite families of double twist knots.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The non-orientable 4-genus of a knot K is the smallest first Betti number of any non-orientable surface in the 4-ball spanning the knot. It is defined to be zero if [&hellip;]<\/p>\n","protected":false},"author":222,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[17],"class_list":["post-3232","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-topology-seminar","cat_topology-seminar"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>On the Non-Orientable 4-Genus of Double Twist Knots, Part II: Lower Bounds (Jim Hoste, Pitzer College) - Claremont Center for the Mathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3232\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"On the Non-Orientable 4-Genus of Double Twist Knots, Part II: Lower Bounds (Jim Hoste, Pitzer College) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"The non-orientable 4-genus of a knot K is the smallest first Betti number of any non-orientable surface in the 4-ball spanning the knot. It is defined to be zero if [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&amp;p=3232\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3232\",\"url\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3232\",\"name\":\"On the Non-Orientable 4-Genus of Double Twist Knots, Part II: Lower Bounds (Jim Hoste, Pitzer College) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/#website\"},\"datePublished\":\"2023-09-13T08:05:34+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3232#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3232\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3232#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Events\",\"item\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/events\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"On the Non-Orientable 4-Genus of Double Twist Knots, Part II: Lower Bounds\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/#website\",\"url\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/\",\"name\":\"Claremont Center for the Mathematical Sciences\",\"description\":\"Proudly Serving the Math Community at the Claremont Colleges Since 2007\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"On the Non-Orientable 4-Genus of Double Twist Knots, Part II: Lower Bounds (Jim Hoste, Pitzer College) - Claremont Center for the Mathematical Sciences","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3232","og_locale":"en_US","og_type":"article","og_title":"On the Non-Orientable 4-Genus of Double Twist Knots, Part II: Lower Bounds (Jim Hoste, Pitzer College) - Claremont Center for the Mathematical Sciences","og_description":"The non-orientable 4-genus of a knot K is the smallest first Betti number of any non-orientable surface in the 4-ball spanning the knot. 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