1,720,979 research outputs found
COMPLEXITIES OF 3-MANIFOLDS FROM TRIANGULATIONS, HEEGAARD SPLITTINGS AND SURGERY PRESENTATIONS
No full textWe study complexities of 3-manifolds defined from triangulations, Heegaard splittings, and surgery presentations. We show that these complexities are related by linear inequalities, by presenting explicit geometric constructions. We also show that our linear inequalities are asymptotically optimal. Our results are used in another paper of the author to estimate Cheeger-Gromov L-2 rho-invariants in terms of geometric group theoretic and knot theoretic data.110sciescopu
Primary decomposition in the smooth concordance group of topologically slice knots
Full text linkWe address primary decomposition conjectures for knot concordance groups,which predict direct sum decompositions into primary parts. We show that thesmooth concordance group of topologically slice knots has a large subgroup forwhich the conjectures are true and there are infinitely many primary parts eachof which has infinite rank. This supports the conjectures for topologicallyslice knots. We also prove analogues for the associated graded groups of thebipolar filtration of topologically slice knots. Among ingredients of theproof, we use amenable -signatures, Ozsv\'ath-Szab\'o -invariants andN\'emethi's result on Heegaard Floer homology of Seifert 3-manifolds. In anappendix, we present a general formulation of the notion of primarydecomposition.<br
Unknotted gropes, Whitney towers, and doubly slicing knots
No full textWe study the structure of the exteriors of gropes and Whitney towers in dimension 4, focusing on their fundamental groups. In particular we introduce a notion of unknottedness of gropes and Whitney towers in the 4-sphere. We prove that various modifications of gropes and Whitney towers preserve the unknottedness and do not enlarge the fundamental group. We exhibit handlebody structures of the exteriors of gropes and Whitney towers constructed by earlier methods of Cochran, Teichner, Horn, and the first author and use them to construct examples of unknotted gropes and Whitney towers. As an application, we introduce geometric bi-filtrations of knots which approximate the double sliceness in terms of unknotted gropes and Whitney towers. We prove that the bi-filtrations do not stabilize at any stage.11Nsciescopu
Rational Whitney tower filtration of links
No full textWe present complete classifications of links in the 3-sphere modulo framed and twisted Whitney towers in a rational homology 4-ball. This provides a geometric characterization of the vanishing of the Milnor invariants of links in terms of Whitney towers. Our result also says that the higher order Arf invariants, which are conjectured to be nontrivial, measure the potential difference between the Whitney tower theory in rational homology 4-balls and that in the 4-ball extensively developed by Conant, Schneiderman and Teichner.110sciescopu
SPLITTING NUMBERS OF LINKS
No full textThe splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering links and Alexander invariants. As an application, we completely determine the splitting numbers of links with nine or fewer crossings. Also, with these techniques, we either reprove or improve upon the lower bounds for splitting numbers of links computed by Batson and Seed using Khovanov homology.111sciescopu
Rasmussen s-invariants of satellites do not detect slice knots
No full textWe present a large family of knots for which the Rasmussen s-invariants of arbitrary satellites do not detect sliceness. This answers a question of Hedden. The proof hinges on work of Kronheimer-Mrowka and Cochran-Harvey-Horn.111Nsciescopu
Two-solvable and two-bipolar knots with large four-genera
Full text linkFor every integer g, we construct a 2-solvable and 2-bipolar knot whosetopological 4-genus is greater than g. Note that 2-solvable knots are inparticular algebraically slice and have vanishing Casson-Gordon obstructions.Similarly all known smooth 4-genus bounds from gauge theory and Floer homologyvanish for 2-bipolar knots. Moreover, our knots bound smoothly embedded heightfour gropes in , an a priori stronger condition than being 2-solvable. Weuse new lower bounds for the 4-genus arising from -signature defectsassociated to meta-metabelian representations of the fundamental group.<br
The bipolar filtration of topologically slice knots
Full text linkThe bipolar filtration of Cochran, Harvey and Horn presents a framework ofthe study of deeper structures in the smooth concordance group of topologicallyslice knots. We show that the graded quotient of the bipolar filtration oftopologically slice knots has infinite rank at each stage greater than one. Todetect nontrivial elements in the quotient, the proof simultaneously useshigher order amenable Cheeger-Gromov -invariants and infinitelymany Heegaard Floer correction term -invariants.<br
ID 기반 암호-서명기법 안전성 증명
No full text학위논문(석사) - 한국정보통신대학교 : 공학부, 2006, [ vi, 57 p. ]After the advent of the concept of provable security, there have been lots of results proving the security of cryptographic schemes theoretically. However, the coverage of those proof is limited to a single scheme. This means that in practice, if somebody congures a combination of two or more schemes, such as encryption and signature, some security vulnerabilities that a scheme compromises the other schemes may happen. So far, there has been few results on a combination of existing cryptographic schemes.
In this paper, we begin a rigorous study of the security of the combination of an encryption scheme and a signature scheme. We give a formal de finitions of the combination of those schemes which we call an encryption-signature (ES). As a variant we also consider an identity-based version which we call an identity-based encryption-signature (IDB-ES). We propose security models of these schemes. Assuming hash functions are random oracles, we prove the security of an IDB-ES scheme obtained by combining a practical identity-based encryption scheme of Boneh-Franklin and signature scheme of Cha-Cheon. Our IDB-ES scheme is secure if Bilinear Di e-Hellman Problem is intractable.한국정보통신대학교 : 공학부
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