Dehn surgeries and negative-definite four-manifolds

Given a knot <i>K</i> in the three-sphere, we address the question: Which Dehn surgeries on <i>K</i> bound negative-definite four-manifolds? We show that the answer depends on a number <i>m(K)</i>, which is a smooth concordance invariant. We study the properties of this invariant and compute it for torus knots

Immersed disks, slicing numbers and concordance unknotting numbers

We study three knot invariants related to smoothly immersed disks in the four-ball. These are the four-ball crossing number, which is the minimal number of normal double points of such a disk bounded by a given knot; the slicing number, which is the minimal number of crossing changes to a slice knot; and the concordance unknotting number, which is the minimal unknotting number in a smooth concordance class. Using Heegaard Floer homology we obtain bounds that can be used to determine two of these invariants for all prime knots with crossing number ten or less, and to determine the concordance unknotting number for all but thirteen of these knots. As a further application we obtain some new bounds on Gordian distance between torus knots. We also give a strengthened version of Ozsvath and Szabo's obstruction to unknotting number one.Comment: 24 pages, 5 figures. V2: added section on Gordian distances between torus knots. V3: Improved exposition incorporating referees' suggestions. Accepted for publication in Comm. Anal. Geo

BOOK REVIEWS

Reviews of; Historical and Cultural Perspectives on Slovenian Migration by Drnovšek Marjan (ed.) (2007) Ljubljana: Institute for Slovenian Emigration Studies, 204 pp. (ISBN 978-961-254-043-2); Migration, Gender and National Identity: Spanish Migrant Women in London Ana Bravo Moreno (2006) Peter Lang, Oxford, Bern, Berlin, Bruxelles, Frankfurt am Main, New York Wien (ISBN 3-03910-156-0). Key words Slovenian migration; Cultural Perspectives; Migration Policy; Migration and Gender; Identity; Spanish migrants; London

Otroštvo v izgnanstvu

Slovenian historiography has to a large degree ignored children and childhood. This disregard seems unjustified, since the lives of young people offer us valuable and often alternative insights into various periods of Slovenian history. The author synthesizes the phenomenon of the wartime exile of Slovenes to neighbouring countries and illustrates it using children’s experiences. Research of children’s experiences of war and exile reflects both the dynamics of wartime migration and the consequences in the Slovenian cultural area. The paper on children’s experiences of exile is placed in the socio-historical context of the Second World War. In terms of methodology it uses a combination of classical historical methodology and oral history; it is based on the relevant historical literature, an analysis of historical materials from throughout the entire post-war era, and various oral testimonies obtained from people in their later years.Slovensko zgodovinopisje je zgodovino otrok in otroštva v veliki meri zapostavilo. Prezrtje se zdi neutemeljeno, saj življenja mladih ponujajo dragocen in pogosto alternativen vpogled v različna obdobja slovenske zgodovine. Avtorica sintetizira fenomen medvojnega izganjanja Slovencev v sosednje države in ga prikazuje skozi otroške izkušnje. Raziskava o otroških izkušnjah vojne in izgonov obenem zrcali medvojno migracijsko dinamiko in njene posledice v slovenskem prostoru. Prispevek o otroških izkušnjah izgnanstva je umeščen v socialno-zgodovinski prikaz druge svetovne vojne. Metodološko prepleta klasično zgodovinsko metodo z metodo ustne zgodovine; temelji na relevantni zgodovinski literaturi, analizi spominskih gradiv, ki je nastajala celotno povojno obdobje, in nekaterih ustnih pričevanj, pridobljenih v zadnjih letih