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Showing 1 to 20 of 355 for “"invariants"”.
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Broken Lefschetz fibrations, Lagrangian matching invariants and Ozsváth-Szabó invariants
… their topology; for instance, Perutz defines invariants of 4-manifolds by counting J-holomorphic sections of these fibrations. The first part of this thesis is about the calculus of these objects. In particular, based on earlier results we prove the existence of broken Lefschetz fibrations on …
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Generalized Dickson invariants
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.
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Connections between Floer-type invariants and Morse-type invariants of Legendrian knots.
We investigate existing Legendrian knot invariants and discover new connections between the theory of generating families, normal rulings and the Chekanov-Eliashberg differential graded algebra: CE-DGA). Given a Legendrian knot $\sK$ with generic front projection $\sfront$, we define a …
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Invariants of Legendrian links
We introduce new, readily computable invariants of Legendrian knots and links in standard contact three-space, allowing us to answer many previously open questions in contact knot theory. The origin of these invariants is the powerful Chekanov-Eliashberg differential graded algebra, which we …
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Cohomological invariants for infinite groups
The main objects of interest in this thesis are H1F-groups. These are groups that act on finite-dimensional contractible CW-spaces with finite stabilisers. Important examples of these are given by groups admitting a finite-dimensional classifying space for proper actions EFG. A large part of the …
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Heegaard Floer Invariants and Cabling
A natural question in knot theory is to ask how certain properties of a knot behave under satellite operations. We will focus on the satellite operation of cabling, and on Heegaard Floer-theoretic properties. In particular, we will give a formula for the Ozsvath-Szabo concordance invariant tau of …
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Circle-Valued Generating Family Invariants
… and Morse theory have been used to define new invariants for Legendrian knots and links in jet spaces of the form J<sup>1</sup>(<em>M</em>, R), where<em> M</em> is a smooth, connected, closed manifold. This dissertation explores the extension of generating families to circle-valued functions, …
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Characteristic Invariants of G-Foliations
Made available in DSpace on 2014-12-14T13:09:32Z (GMT). No. of bitstreams: 1 7708979.pdf: 3908134 bytes, checksum: aaffce1a2fed4827139c5a5793cd7e20 (MD5) Previous issue date: 1976
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Testing in learning conjunctive invariants
We show a new approach in learning conjunctive invariants using dynamic testing of the program. Coming up with correct set of loop invariant is the most challenging part of any verification methods. Although new methods tend to generate a large number of possible invariants hoping this set contains …
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Topological invariants of symplectic quotients
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.
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Partially Ordered Sets and Their Invariants
We investigate how much information cardinal invariants can give on the structure of the ordered set on which they are de�ned. We consider the basic de�nitions of an ordered set and see how they are related to one another. We generalize some results on cardinal invariants for ordered sets and state …
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Homological invariants of some special varieties
… several different results about some homological invariants (e.g., graded Betti numbers, Hilbert function, regularity) of some special varieties. In particular, we focus on the codimension two ACM varieties in P1×P1×P1 (called varieties of lines), and the edge ideals of bicyclic graphs. We study …
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Dual Homotopy Invariants of G-Foliations
This thesis defines and studies a new set of invariants for a foliation on a manifold M, where the normal bundle of is assumed to have a parallel G-structure. As an application of the theory which is constructed, it is shown that many of the secondary characteristic classes of smooth foliations are …
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Generalized Kummer congruences and Iwasawa invariants
We obtain the following generalization of the Kummer congruence: $$G\sb{c}(j,\chi,n) = -\left\lbrack{p\sp{-1}\Delta\sb{\rm c}\atop j}\right\rbrack {1\over n}(1 - \chi\omega\sp{-n}(p)\ p\sp{n-1}) B\sb{n,\chi\omega\sp{-n}}\in\doubz\sb{p}\lbrack\chi\rbrack ,$$where $B\sb{n,\chi}$ is the generalized …
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Learning inductive invariants using Winnow algorithm
… algorithm, Winnow-ICE, to synthesize inductive invariants for proving that a program is correct by validating its assertions. Winnow is an online learning algorithm that can be used to learn Boolean formulae from positive, negative and implication counterexamples. We implemented the Winnow …
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Expression and localization of object invariants
Thesis (S.B. and M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.
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Ozsva?th-Szabo? invariants of contact surgeries
… Floer homology, by computing their Ozsvath-Szab6 invariants. It's a classical result that doing negative contact surgeries along Legendrian links in ( S3, tst) yields back tight (in fact, Stein fillable) contact structures, so I am going to discuss positive contact surgeries. The main result gives …
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