| 1. |
- Abouzaid, Mohammed, et al.
(författare)
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On the immersion classes of nearby Lagrangians
- 2016
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Ingår i: Journal of Topology. - : Wiley. - 1753-8416 .- 1753-8424. ; 9:1, s. 232-244
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Tidskriftsartikel (refereegranskat)abstract
- We show that the transfer map on Floer homotopy types associated to an exact Lagrangian embedding is an equivalence. This provides an obstruction to representing isotopy classes of Lagrangian immersions by Lagrangian embeddings, which, unlike previous obstructions, is sensitive to information that cannot be detected by Floer cochains. We show this by providing a concrete computation in the case of spheres.
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| 2. |
- Aceto, Paolo, et al.
(författare)
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Embedding 3-manifolds in spin 4-manifolds
- 2017
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Ingår i: Journal of Topology. - : WILEY. - 1753-8416 .- 1753-8424. ; 10:2, s. 301-323
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Tidskriftsartikel (refereegranskat)abstract
- An invariant of orientable 3-manifolds is defined by taking the minimum n such that a given 3-manifold embeds in the connected sum of n copies of S-2 x S-2, and we call this n the embedding number of the 3-manifold. We give some general properties of this invariant, and make calculations for families of lens spaces and Brieskorn spheres. We show how to construct rational and integral homology spheres whose embedding numbers grow arbitrarily large, and which can be calculated exactly if we assume the 11/8-Conjecture. In a different direction we show that any simply connected 4-manifold can be split along a rational homology sphere into a positive definite piece and a negative definite piece.
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| 3. |
- Bergström, Jonas, et al.
(författare)
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The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three
- 2008
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Ingår i: Journal of Topology. - : Wiley. - 1753-8416 .- 1753-8424. ; 1:3, s. 651-662
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Tidskriftsartikel (refereegranskat)abstract
- We show how to calculate the Euler characteristic of a local system V(lambda) associated to an irreducible representation V(lambda) of the symplectic group of genus 3 on the moduli space M(3) of curves of genus 3 and the moduli space A(3) of principally polarised abelian varieties of dimension 3.
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| 4. |
- Bucher-Karlsson, Michelle
(författare)
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The simplicial volume of closed manifolds covered by H-2 x H-2
- 2008
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Ingår i: Journal of Topology. - : Wiley. - 1753-8416 .- 1753-8424. ; 1:3, s. 584-602
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Tidskriftsartikel (refereegranskat)abstract
- We compute the value of the simplicial volume for closed, oriented Riemannian manifolds covered by H-2 x H-2 explicitly, and thus in particular for products of closed hyperbolic surfaces. This gives the first exact value of a nonvanishing simplicial volume for a manifold not admitting a hyperbolic structure.
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| 5. |
- Deeley, Robin J., et al.
(författare)
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Relative geometric assembly and mapping cones, part I: the geometric model and applications
- 2018
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Ingår i: Journal of Topology. - : Wiley. - 1753-8416 .- 1753-8424. ; 11:4, s. 966-1000
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Tidskriftsartikel (refereegranskat)abstract
- Inspired by an analytic construction of Chang, Weinberger and Yu, we define an assembly map in relative geometric K-homology. The properties of the geometric assembly map are studied using a variety of index theoretic tools (for example, the localized index and higher Atiyah–Patodi–Singer index theory). As an application we obtain a vanishing result in the context of manifolds with boundary and positive scalar curvature; this result is also inspired and connected to the work of Chang, Weinberger and Yu. Furthermore, we use results of Wahl to show that rational injectivity of the relative assembly map implies homotopy invariance of the relative higher signatures of a manifold with boundary.
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| 6. |
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| 7. |
- Diogo, Luis, et al.
(författare)
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Symplectic homology of complements of smooth divisors
- 2019
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Ingår i: Journal of Topology. - : Wiley. - 1753-8416 .- 1753-8424. ; 12:3, s. 967-1030
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Tidskriftsartikel (refereegranskat)abstract
- If (X,omega) is a closed symplectic manifold, and sigma is a smooth symplectic submanifold Poincare dual to a positive multiple of omega, then X set minus sigma can be completed to a Liouville manifold (W,d lambda). Under monotonicity assumptions on X and on sigma, we construct a chain complex whose homology computes the symplectic homology of W. We show that the differential is given in terms of Morse contributions, Gromov-Witten invariants of X relative to sigma and Gromov-Witten invariants of sigma. We use a Morse-Bott model for symplectic homology. Our proof involves comparing Floer cylinders with punctures to pseudoholomorphic curves in the symplectization of the unit normal bundle to sigma.
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| 8. |
- Ekholm, Tobias, 1970-
(författare)
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Non-loose Legendrian spheres with trivial contact homology DGA
- 2016
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Ingår i: Journal of Topology. - : Wiley. - 1753-8416 .- 1753-8424. ; 9:3, s. 826-848
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Tidskriftsartikel (refereegranskat)abstract
- Loose Legendrian n-submanifolds, n >= 2, were introduced by Murphy ('Loose Legendrian embeddings in high dimensional contact manifolds', Preprint, 2012, arXiv:1201.2245) and proved to be flexible in the h-principle sense: any two loose Legendrian submanifolds that are formally Legendrian isotopic are also actually Legendrian isotopic. Legendrian contact homology is a Floer theoretic invariant that associates a differential graded algebra (DGA) to a Legendrian submanifold. The DGA of a loose Legendrian submanifold is trivial. We show that the converse is not true by constructing non-loose Legendrian n-spheres in standard contact (2n + 1)-space, n >= 2, with trivial DGA.
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| 9. |
- Hall, Jack, et al.
(författare)
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The telescope conjecture for algebraic stacks
- 2017
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Ingår i: Journal of Topology. - : Wiley. - 1753-8416 .- 1753-8424. ; 10:3, s. 776-794
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Tidskriftsartikel (refereegranskat)abstract
- Using Balmer-Favi's generalized idempotents, we establish the telescope conjecture for many algebraic stacks. Along the way, we classify the thick tensor ideals of perfect complexes of stacks.
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| 10. |
- Lang, Lionel
(författare)
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Monodromy of rational curves on toric surfaces
- 2020
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Ingår i: Journal of Topology. - : London Mathematical Society. - 1753-8416 .- 1753-8424. ; 13:4, s. 1658-1681
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Tidskriftsartikel (refereegranskat)abstract
- For an ample line bundle L on a complete toric surface X, we consider the subset VL subset of|L| of irreducible, nodal, rational curves contained in the smooth locus of X. We study the monodromy map from the fundamental group of VL to the permutation group on the set of nodes of a reference curve C is an element of VL. We identify a certain obstruction map psi X defined on the set of nodes of C and show that the image of the monodromy is exactly the group of deck transformations of psi X, provided that L is sufficiently big (in the sense we make precise below). Along the way, we construct a handy tool to compute the image of the monodromy for any pair (X,L). Eventually, we present a family of pairs (X,L) with small L and for which the image of the monodromy is strictly smaller than expected.
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