Fibering Five Manifolds Over A Circle.
dc.contributor.author | Hsu, Chang-wang Felix | |
dc.date.accessioned | 2016-08-30T16:38:02Z | |
dc.date.available | 2016-08-30T16:38:02Z | |
dc.date.issued | 1985 | |
dc.identifier.uri | http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:8600458 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/127805 | |
dc.description.abstract | In this thesis, after we update some basic facts about 4- manifolds and the smoothings of 4 dimensional manifolds we prove the following: Technical Lemma. Given a 5-dimensional compact cobordism (W;V(,1),V(,2)) satisfying: (a) Int(W) is smooth, (b) W, V(,1), V(,2) are 1-connected, (c) H(,2)(W,V(,1)) = <(alpha)(,1),...,(alpha)(,j)>, H(,2)(W,V(,2)) = <(')(beta)(,1),...,(')(beta)(,k)> are free abelian of rank j, k respectively, and (d) H(,3)(W) = 0 and H(,2)(W) is free abelin; then (1) j = k, (2) V(,1) = V(,0) # k(S('2) x S('2)) where V(,0) is a closed, 1-connected topological 4-manifold. Similarly V(,2) is the sum of a closed 1-connected manifold and k copies of (S('2) x S('2)). (3) Each generator of H(,3)(W,V(,1)) = <b(,1),...,b(,k)> can be represented as a 3-handle. We then use this lemma to deduce the following fibering theorem: Theorem. If W is a smooth closed 5-manifold with (pi)(,1)(W) = , and H(,*)((')W) is finitely-generated, then W fibers over a circle with fiber a 1-connected topological 4-manifold. As a second application, we use our technical lemma to provide a unified proof for some well-known theorems in 5-dimensional knot theory. We conclude with an interesting corollary which should shed some light on the classification of closed, oriented smooth 5-manifolds with (pi)(,1) = . Corollary. The closed, connected, orientable 5-manifolds M with (pi)(,1)(M) = and H(,2)(M) (TBOND) 0 are completely classified by their Milnor forms, hence they are classified by their Blanchfield forms also. | |
dc.format.extent | 104 p. | |
dc.language | English | |
dc.language.iso | EN | |
dc.subject | Circle | |
dc.subject | Fibering | |
dc.subject | Five | |
dc.subject | Manifolds | |
dc.subject | Over | |
dc.title | Fibering Five Manifolds Over A Circle. | |
dc.type | Thesis | |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Mathematics | |
dc.description.thesisdegreediscipline | Pure Sciences | |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/127805/2/8600458.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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