The very last PhD thesis from Bangor (for the foreseeable future) is now available on the website. In it Richard Lewis looks at the problem of the interpretation of the formal maps to a crossed module introduced by Porter and Turaev and using a simplicial analogue of etale spaces gets a representation in terms of locally constant stacks. The links is http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/0= 7/cathom07.html#07.09 All for now, Tim PS. The abstract follows Stacks and formal maps of crossed modules Abstract: If X is a topological space then there is an equivalence between the category \pi_1(X)-Set, of actions of the fundamental group of X on sets, and the category of covering spaces on X. Moreover the latter is also equivalent to the category of locally constant sheaves on X. Grothendieck has conjectured that this should be the 'n=3D1' case of a result which is true for all n, and it is the 'n=3D2' case we look at in this thesis. The desired generalisation should replace actions of the group \pi_1(X) (which is an algebraic model for the 1-type of X) by actions of a crossed module (i.e., by an algebraic model for the 2-type) on groupoids; 'locally constant sheaves of sets' by 'locally constant stacks of groupoids'; and 'covering space' by a locally trivial object whose fibres are groupoids. This last object we handle using the machinery of simplicial fibre bundles (twisted Cartesian products) and formal maps, building a simplicial object, Z(\lambda), where the fibre is now a (nerve of) a groupoid. To interpret Z(\lambda) as a stack, we show that just as sheaves on X are equivalent to etale spaces, we can define a notion of 2-etale space corresponding to stacks and show that from Z(\lambda) we can construct a locally constant stack on X. --=20 Gall y neges e-bost hon, ac unrhyw atodiadau a anfonwyd gyda hi, gynnwys deunydd cyfrinachol ac wedi eu bwriadu i'w defnyddio'n unig gan y sawl y cawsant eu cyfeirio ato (atynt). Os ydych wedi derbyn y neges e-bost hon trwy gamgymeriad, rhowch wybod i'r anfonwr ar unwaith a dil=EBwch y neges. Os na fwriadwyd anfon y neges atoch chi, rhaid i chi beidio =E2 defnyddio, cadw neu ddatgelu unrhyw wybodaeth a gynhwysir ynddi. Mae unrhyw farn neu safbwynt yn eiddo i'r sawl a'i hanfonodd yn unig ac nid yw o anghenraid yn cynrychioli barn Prifysgol Cymru, Bangor. Nid yw Prifysgol Cymru, Bangor yn gwarantu bod y neges e-bost hon neu unrhyw atodiadau yn rhydd rhag firysau neu 100% yn ddiogel. Oni bai fod hyn wedi ei ddatgan yn uniongyrchol yn nhestun yr e-bost, nid bwriad y neges e-bost hon yw ffurfio contract rhwymol - mae rhestr o lofnodwyr awdurdodedig ar gael o Swyddfa Cyllid Prifysgol Cymru, Bangor. www.bangor.ac.uk (YCYG) This email and any attachments may contain confidential material and is solely for the use of the intended recipient(s). If you have received this email in error, please notify the sender immediately and delete this email. If you are not the intended recipient(s), you must not use, retain or disclose any information contained in this email. Any views or opinions are solely those of the sender and do not necessarily represent those of the University of Wales, Bangor. The University of Wales, Bangor does not guarantee that this email or any attachments are free from viruses or 100% secure. Unless expressly stated in the body of the text of the email, this email is not intended to form a binding contract - a list of authorised signatories is available from the University of Wales, Bangor Finance Office. www.bangor.ac.uk (SEECS)