{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T03:25:59Z","timestamp":1649215559087},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1998,2]]},"abstract":"<jats:p> Let G be a finitely generated group. The Bieri\u2013Neumann\u2013Strebel invariant \u03a3<jats:sup>1<\/jats:sup>(G) of G determines, among other things, the distribution of finitely generated subgroups N\u25c3G with G\/N abelian. This invariant can be quite difficult to compute. Given a finite presentation \u3008S:R\u3009 for G, there is an algorithm, introduced by Brown and extended by Bieri and Strebel, which determines a space \u03a3(R) that is always contained in, and is sometimes equal to, \u03a3<jats:sup>1<\/jats:sup>(G). We refine this algorithm to one which involves the local structure of the universal cover of the standard 2-complex of a given presentation. Let \u03a8(R) denote the space determined by this algorithm. We show that \u03a3(R) \u2286 \u03a8 \u2286 \u03a3<jats:sup>1<\/jats:sup>(G) for any finitely presented group G, and if G admits a staggered presentation, then \u03a8 = \u03a3<jats:sup>1<\/jats:sup>(G). By casting this algorithm in terms of connectivity properties of graphs, it is shown to be computationally feasible. <\/jats:p>","DOI":"10.1142\/s021819679800003x","type":"journal-article","created":{"date-parts":[[2003,7,31]],"date-time":"2003-07-31T06:08:41Z","timestamp":1059631721000},"page":"23-34","source":"Crossref","is-referenced-by-count":1,"title":["Whitehead Graphs and the \u03a3<sup>1<\/sup>-Invariants of Infinite Groups"],"prefix":"10.1142","volume":"08","author":[{"given":"Susan Garner","family":"Garille","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lafayette College, Easton, PA 18042, USA"}]},{"given":"John","family":"Meier","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lafayette College, Easton, PA 18042, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389175"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389176"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(87)90015-6"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02621931"},{"key":"p_6","first-page":"15","volume":"8","author":"Gersten S. M.","year":"1987","journal-title":"MSRI Publications"},{"key":"p_7","first-page":"53","volume":"111","author":"Howie J.","year":"1987","journal-title":"Annals of Mathematics Studies"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388491"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.2307\/1969440"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(95)00100-B"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1112\/S0024611597000063"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-71.2.263"},{"key":"p_14","first-page":"95","author":"Stallings J.","year":"1962","journal-title":"Prentice-Hall"},{"key":"p_15","first-page":"1","volume":"4","author":"J. H.","year":"1936","journal-title":"Proc. London Math. Soc."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819679800003X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:53:35Z","timestamp":1565114015000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819679800003X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,2]]},"references-count":13,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1998,2]]}},"alternative-id":["10.1142\/S021819679800003X"],"URL":"https:\/\/doi.org\/10.1142\/s021819679800003x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,2]]}}}