oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
Quandles and Monodromy  [PDF]
D. N. Yetter
Mathematics , 2002,
Abstract: We show that a variety of monodromy phenomena arising in geometric topology and algebraic geometry are most conveniently described in terms of quandle homomorphisms from a knot quandle associated to the base to a quandle associated to a fiber. We consider the cases of the monodromy of a branched covering, braid monodromy and the monodromy of a Lefschetz fibration.
Quandles and Lefschetz Fibrations  [PDF]
D. N. Yetter
Mathematics , 2002,
Abstract: We show that isotopy classes of simple closed curves in any oriented surface admit a quandle structure with operations induced by Dehn twists, the Dehn quandle of the surface. We further show that the monodromy of a Lefschetz fibration can be conveniently encoded as a quandle homomorphism from the knot quandle of the base as a manifold with a codimension 2 subspace (the set of singular values) to the Dehn quandle of the generic fibre, and discuss prospects for construction of invariants arising naturally from this description of the monodromy.
The Picard-Lefschetz formula and a conjecture of Kato, the case of Lefschetz fibrations  [PDF]
Caterina Consani,Minhyong Kim
Mathematics , 2002,
Abstract: A conjecture of Kato says that the monodromy operator on the cohomology of a semi-stable degeneration of projective varieties is represented by an algebraic cycle on the special fiber of a normal crossing model of the fiber product degeneration. We prove this conjecture in the simple case of a semi-stable degeneration arising from a Lefschetz fibration.
Lagrangian torus fibration of quintic Calabi-Yau hypersurfaces I: Fermat quintic case  [PDF]
Wei-Dong Ruan
Mathematics , 1999,
Abstract: In this paper we give a construction of Lagrangian torus fibration for Fermat type quintic \cy hypersurfaces via the method of gradient flow. We also compute the monodromy of the expected special Lagrangian torus fibration and discuss structures of singular fibers.
A genus zero Lefschetz fibration on the Akbulut cork  [PDF]
Takuya Ukida
Mathematics , 2014,
Abstract: We first construct a genus zero positive allowable Lefschetz fibration over the disk (a genus zero PALF for short) on the Akbulut cork and describe the monodromy as a positive factorization in the mapping class group of a surface of genus zero with five boundary components. We then construct genus zero PALFs on infinitely many exotic pairs of compact Stein surfaces such that one is a cork twist of the other along an Akbulut cork. The difference of smooth structures on each of exotic pairs of compact Stein surface is interpreted as the difference of the corresponding positive factorizations in the mapping class group of a common surface of genus zero.
Chart description for hyperelliptic Lefschetz fibrations and their stabilization  [PDF]
Hisaaki Endo,Seiichi Kamada
Mathematics , 2013,
Abstract: Chart descriptions are a graphic method to describe monodromy representations of various topological objects. Here we introduce a chart description for hyperelliptic Lefschetz fibrations, and show that any hyperelliptic Lefschetz fibration can be stabilized by fiber-sum with certain basic Lefschetz fibrations.
Signatures of Lefschetz fibrations  [PDF]
Burak Ozbagci
Mathematics , 1998,
Abstract: Let M be a smooth 4-manifold which admits a genus g Lefschetz fibration over D^2 or S^2. We develop a technique to compute the signature of M using the global monodromy of this fibration.
Chart description for genus-two Lefschetz fibrations and a theorem on their stabilization  [PDF]
Seiichi Kamada
Mathematics , 2011,
Abstract: Chart descriptions are a graphic method to describe monodromy representations of various topological objects. Here we introduce a chart description for genus-two Lefschetz fibrations, and show that any genus-two Lefschetz fibration can be stabilized by fiber-sum with certain basic Lefschetz fibrations.
Lefschetz numbers of iterates of the monodromy and truncated arcs  [PDF]
J. Denef,F. Loeser
Mathematics , 2000,
Abstract: We express the Lefschetz number of iterates of the monodromy of a function on a smooth complex algebraic variety in terms of the Euler characteristic of a space of truncated arcs.
Monodromy and the Lefschetz fixed point formula  [PDF]
E. Hrushovski,F. Loeser
Mathematics , 2011,
Abstract: We give a new proof - not using resolution of singularities - of a formula of Denef and the second author expressing the Lefschetz number of iterates of the monodromy of a function on a smooth complex algebraic variety in terms of the Euler characteristic of a space of truncated arcs. Our proof uses l-adic cohomology of non-archimedean spaces, motivic integration and the Lefschetz fixed point formula for finite order automorphisms. We also consider a generalization due to Nicaise and Sebag and at the end of the paper we discuss connections with the motivic Serre invariant and the motivic Milnor fiber.
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.