Edinburgh Research Archive logo

Edinburgh Research Archive

University of Edinburgh homecrest
View Item 
  •   ERA Home
  • Mathematics, School of
  • Mathematics thesis and dissertation collection
  • View Item
  •   ERA Home
  • Mathematics, School of
  • Mathematics thesis and dissertation collection
  • View Item
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.

Second order algebraic knot concordance group

View/Open
Joint papers with Stefan Friedl submitted for publication.zip (444.2Kb)
Thesis Figures.zip (3.776Mb)
Thesis Latex Source Files.zip (135.7Kb)
Powell2011.pdf (1.429Mb)
Date
28/06/2011
Author
Powell, Mark Andrew
Metadata
Show full item record
Abstract
Let Knots be the abelian monoid of isotopy classes of knots S1 ⊂ S3 under connected sum, and let C be the topological knot concordance group of knots modulo slice knots. Cochran-Orr-Teichner [COT03] defined a filtration of C: C ⊃ F(0) ⊃ F(0.5) ⊃ F(1) ⊃ F(1.5) ⊃ F(2) ⊃ . . .The quotient C/F(0.5) is isomorphic to Levine’s algebraic concordance group AC1 [Lev69]; F(0.5) is the algebraically slice knots. The quotient C/F(1.5) contains all metabelian concordance obstructions. The Cochran-Orr-Teichner (1.5)-level two stage obstructions map the concordance class of a knot to a pointed set (COT (C/1.5),U). We define an abelian monoid of chain complexes P, with a monoid homomorphism Knots → P. We then define an algebraic concordance equivalence relation on P and therefore a group AC2 := P/ ~, our second order algebraic knot concordance group. The results of this thesis can be summarised in the following diagram: . That is, we define a group homomorphism C → AC2 which factors through C/F(1.5). We can extract the two stage Cochran-Orr-Teichner obstruction theory from AC2: the dotted arrows are morphisms of pointed sets. Our second order algebraic knot concordance group AC2 is a single stage obstruction group.
URI
http://hdl.handle.net/1842/5030
Collections
  • Mathematics thesis and dissertation collection

Library & University Collections HomeUniversity of Edinburgh Information Services Home
Privacy & Cookies | Takedown Policy | Accessibility | Contact
Privacy & Cookies
Takedown Policy
Accessibility
Contact
feed RSS Feeds

RSS Feed not available for this page

 

 

All of ERACommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsPublication TypeSponsorSupervisorsThis CollectionBy Issue DateAuthorsTitlesSubjectsPublication TypeSponsorSupervisors
LoginRegister

Library & University Collections HomeUniversity of Edinburgh Information Services Home
Privacy & Cookies | Takedown Policy | Accessibility | Contact
Privacy & Cookies
Takedown Policy
Accessibility
Contact
feed RSS Feeds

RSS Feed not available for this page