{"abstracts":[{"sha1":"d0230dd5806028e198b92edc1912f7aa7b393d61","content":"The notion of a Bing cell is introduced, and it is used to define invariants,\nlink groups, of 4-manifolds. Bing cells combine some features of both surfaces\nand 4-dimensional handlebodies, and the link group \\lambda(M) measures certain\naspects of the handle structure of a 4-manifold M. This group is a quotient of\nthe fundamental group, and examples of manifolds are given with \\pi_1(M) not\nequal to \\lambda(M). The main construction of the paper is a generalization of\nthe Milnor group, which is used to formulate an obstruction to embeddability of\nBing cells into 4-space. Applications to the A-B slice problem and to the\nstructure of topological arbiters are discussed.","mimetype":"text/plain","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Vyacheslav Krushkal","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v2","ext_ids":{"arxiv":"math/0510507v2"},"release_year":2011,"release_date":"2011-10-01","release_stage":"submitted","release_type":"article","webcaptures":[],"filesets":[],"files":[{"release_ids":["pyprcqfkbfd7bgke2m44eknrii"],"mimetype":"application/pdf","urls":[{"url":"https://arxiv.org/pdf/math/0510507v2.pdf","rel":"repository"},{"url":"https://web.archive.org/web/20200904125827/https://arxiv.org/pdf/math/0510507v2.pdf","rel":"webarchive"}],"sha256":"23aeb0aaf8402e475b6b34a6804e7a11b921678af1f8147a9bf5e1bc16a6b1fb","sha1":"7a7373e090bda1a4982ca4fb522f7675d0847210","md5":"0302cadb6363ae56ff6e650073620f8b","size":676319,"revision":"4ef05fea-7448-4fa0-a668-db3f6d782dcc","ident":"3xebnod5hrgx3dinoznmj6mib4","state":"active"}],"work_id":"wf7ufgesuzghnpxek533zi4azi","title":"Link groups of 4-manifolds","state":"active","ident":"pyprcqfkbfd7bgke2m44eknrii","revision":"06ff4f83-24b1-4fe6-b343-27e4bfd505cd","extra":{"arxiv":{"base_id":"math/0510507","categories":["math.GT"],"comments":"34 pages, 7 figures. v.3: minor phrasing changes","journal_ref":"Proceedings of the Freedman Fest, 199-234, Geom. Topol. Monogr.,\n 18, Coventry, 2012"},"superceded":true}}