Theses - Mathematics
http://hdl.handle.net/1721.1/7842
Tue, 09 Feb 2016 05:50:14 GMT2016-02-09T05:50:14ZRestriction to hypersurfaces of non-isotropic Sobolev spaces
http://hdl.handle.net/1721.1/100868
Restriction to hypersurfaces of non-isotropic Sobolev spaces
Mekias, Mohamed
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1993.; Includes bibliographical references (leaves 67-68).
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/1721.1/1008681993-01-01T00:00:00ZOn integral equations, their solution by iteration and analytic continuation
http://hdl.handle.net/1721.1/100072
On integral equations, their solution by iteration and analytic continuation
Perlis, Alan J
Thesis (Ph.D.) Massachusetts Institute of Technology. Dept. of Mathematics, 1950.; Vita.; Bibliography: leaves 65-66.
Sun, 01 Jan 1950 00:00:00 GMThttp://hdl.handle.net/1721.1/1000721950-01-01T00:00:00ZThe v₁-periodic part of the Adams spectral sequence at an odd prime/
http://hdl.handle.net/1721.1/99328
The v₁-periodic part of the Adams spectral sequence at an odd prime/
Andrews, Michael Joseph, Ph. D. Massachusetts Institute of Technology
We tell the story of the stable homotopy groups of spheres for odd primes at chromatic height 1 through the lens of the Adams spectral sequence. We find the "dancers to a discordant system." We calculate a Bockstein spectral sequence which converges to the 1-line of the chromatic spectral sequence for the odd primary Adams E₂-page. Furthermore, we calculate the associated algebraic Novikov spectral sequence converging to the 1-line of the BP chromatic spectral sequence. This result is also viewed as the calculation of a direct limit of localized modified Adams spectral sequences converging to the homotopy of the v1 -periodic sphere spectrum. As a consequence of this work, we obtain a thorough understanding of a collection of q₀-towers on the Adams E₂-page and we obtain information about the differentials between these towers. Moreover, above a line of slope 1/(p²-p-1) we can completely describe the E₂ and E₃ -pages of the mod p Adams spectral sequence, which accounts for almost all the spectral sequence in this range.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.; In title on title-page, "v" is italicized, and "1" is subscript. Cataloged from PDF version of thesis.; Includes bibliographical references (pages 139-140).
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/1721.1/993282015-01-01T00:00:00ZUnstable operations in the Bousfield-Kan spectral sequence for simplicial commutative FF₂-algebras
http://hdl.handle.net/1721.1/99327
Unstable operations in the Bousfield-Kan spectral sequence for simplicial commutative FF₂-algebras
Donovan, Michael Jack
In this thesis we study the Bousfield-Kan spectral sequence (BKSS) in the Quillen model category sCom of simplicial commutative FF₂ -algebras. We develop a theory of unstable operations for this BKSS and relate these operations with the known unstable operations on the homotopy of the target. We also prove a completeness theorem and a vanishing line theorem which, together, show that the BKSS for a connected object of sCom converges strongly to the homotopy of that object. We approach the computation of the BKSS by deriving a composite functor spectral sequence (CFSS) which converges to the BKSS E2 -page. In fact, we generalize the construction of this CFSS to yield an infinite sequence of CFSSs, with each converging to the E2-page of the previous. We equip each of these CFSSs with a theory of unstable spectral sequence operations, after establishing the necessary chain-level structure on the resolutions defining the CFSSs. This technique may also yield operations on Blanc and Stover's generalized Grothendieck spectral sequences in other settings. We are able to compute the Bousfield-Kan E2-page in the most fundamental case, that of a connected sphere in sCom, using the structure defined on the CFSSs. We use this computation to describe the Ei-page of a May-Koszul spectral sequence which converges to the BKSS E2-page for any connected object of sCom. We conclude by making two conjectures which would, together, allow for a full computation of the BKSS for a connected sphere in sCom.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 219-222).
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/1721.1/993272015-01-01T00:00:00Z