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Geometric Topology

New submissions

[ total of 14 entries: 1-14 ]
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New submissions for Tue, 20 Mar 18

[1]  arXiv:1803.06382 [pdf, ps, other]
Title: Harmonic spinors on the Davis hyperbolic 4-manifold
Comments: 33 pages and 2 figures
Subjects: Geometric Topology (math.GT); Differential Geometry (math.DG)

In this paper we use the G-spin theorem to show that the Davis hyperbolic 4-manifold admits harmonic spinors. This is the first example of a closed hyperbolic 4-manifold that admits harmonic spinors. We also explicitly describe the Spinor bundle of a spin hyperbolic 2- or 4-manifold and show how to calculated the subtle sign terms in the G-spin theorem for an isometry, with isolated fixed points, of a closed spin hyperbolic 2- or 4-manifold.

[2]  arXiv:1803.06455 [pdf, ps, other]
Title: A-infinity algebras, strand algebras, and contact categories
Comments: 83 pages, 23 figures, 6 tables
Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT); Symplectic Geometry (math.SG)

In previous work we showed that the contact category algebra of a quadrangulated surface is isomorphic to the homology of a strand algebra from bordered Floer theory. Being isomorphic to the homology of a differential graded algebra, this contact category algebra has an A-infinity structure. In this paper we investigate such A-infinity structures in detail. We give explicit constructions of such A-infinity structures, and establish some of their properties, including conditions for the nonvanishing of A-infinity operations. Along the way we develop several related notions, including a detailed consideration of tensor products of strand diagrams.

[3]  arXiv:1803.06470 [pdf, ps, other]
Title: Twisted Alexander Polynomials of $(-2,3,2n+1)$-Pretzel Knots
Authors: Airi Aso
Comments: 8 pages, 2 figures
Subjects: Geometric Topology (math.GT)

We calculate the twisted Alexander polynomials of $(-2,3,2n+1)$-pretzel knots associated to their holonomy representations. As a corollary, we obtain new supporting evidences of Dunfield, Friedl and Jackson's conjecture, that is, the twisted Alexander polynomials of hyperbolic knots associated to their holonomy representations determine the genus and fiberedness of the knots.

[4]  arXiv:1803.06713 [pdf, other]
Title: Four-manifolds with shadow-complexity one
Comments: 75 pages, 77 figures
Subjects: Geometric Topology (math.GT)

We study the set of all closed oriented smooth 4-manifolds experimentally, according to a suitable complexity defined using Turaev shadows. This complexity roughly measures how complicated the 2-skeleton of the 4-manifold is. We characterise all the closed oriented 4-manifolds that have complexity $\leq 1$. These are precisely the 4-manifolds that are generated by a certain set of 20 blocks, that is some basic 4-manifolds with boundary consisting of copies of $S^2 \times S^1$, plus connected sums with some copies of $\mathbb {CP}^2$ with either orientation.

[5]  arXiv:1803.06870 [pdf, ps, other]
Title: An invitation to higher Teichmüller theory
Authors: Anna Wienhard
Comments: written for the Proceedings of the ICM
Subjects: Geometric Topology (math.GT)

The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.

Cross-lists for Tue, 20 Mar 18

[6]  arXiv:1708.04108 (cross-list from math.SG) [pdf, other]
Title: Obstructions to planarity of contact 3-manifolds
Comments: 24 pages, 8 figures; major revision: we added new statements, and improved the exposition of the old ones. Comments are welcome!
Subjects: Symplectic Geometry (math.SG); Geometric Topology (math.GT)

We prove that if a contact 3-manifold admits an open book decomposition of genus 0, a certain intersection pattern cannot appear in the homology of any of its symplectic fillings, and morever, fillings cannot contain certain symplectic surfaces. Applying these obstructions to canonical contact structures on links of normal surface singularities, we show that links of isolated singularities of surfaces in the complex 3-space are planar only in the case of $A_n$-singularities, and in general characterize completely planar links of normal surface singularities (in terms of their resolution graphs). We also establish non-planarity of tight contact structures on certain small Seifert fibered L-spaces and of contact structures compatible with open books given by a boundary multi-twist on a page of positive genus. Additionally, we prove that every finitely presented group is the fundamental group of a Leschetz fibration with planar fibers.

Replacements for Tue, 20 Mar 18

[7]  arXiv:1608.08163 (replaced) [pdf, ps, other]
Title: Singular Knots and Involutive Quandles
Comments: 13 pages; v4 adds axioms required for symmetry at unoriented singular crossings
Subjects: Geometric Topology (math.GT); Quantum Algebra (math.QA)
[8]  arXiv:1708.04853 (replaced) [pdf, other]
Title: A polynomial time knot polynomial
Comments: Typos fixed, length reduced for publication in PAMS
Subjects: Geometric Topology (math.GT)
[9]  arXiv:1712.00434 (replaced) [pdf, other]
Title: On the treewidth of triangulated 3-manifolds
Comments: 23 pages, 3 figures, 1 table. An extended abstract of this paper is to appear in the Proceedings of the 34th International Symposium on Computational Geometry (SoCG 2018), Budapest, June 11-14 2018
Subjects: Geometric Topology (math.GT); Computational Geometry (cs.CG); Combinatorics (math.CO)
[10]  arXiv:1801.00335 (replaced) [pdf, ps, other]
Title: Plato's cave and differential forms
Authors: Fedor Manin
Comments: 33 pages, 1 figure; comments welcome! This version corrects an error pointed out by A. Berdnikov
Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT); Differential Geometry (math.DG); Metric Geometry (math.MG)
[11]  arXiv:1802.03186 (replaced) [pdf, ps, other]
Title: A simplification problem in manifold theory
Comments: 35 pages. Small improvements and new references
Subjects: Geometric Topology (math.GT)
[12]  arXiv:1803.05116 (replaced) [pdf, ps, other]
Title: Extending automorphisms of the genus-2 surface over the 3-sphere
Comments: 21 pages, 15 fugures; typos corrected
Subjects: Geometric Topology (math.GT)
[13]  arXiv:1704.08485 (replaced) [pdf, ps, other]
Title: 2-Verma modules and the Khovanov-Rozansky link homologies
Comments: v1, 32 pages, colored figures. v2, 42 pages, Proof of the main result expanded into a new subsection, minor corrections
Subjects: Quantum Algebra (math.QA); Geometric Topology (math.GT); Representation Theory (math.RT)
[14]  arXiv:1802.07049 (replaced) [pdf, ps, other]
Title: The Bieri-Neumann-Strebel invariants via Newton polytopes
Authors: Dawid Kielak
Comments: 39 pages, no figures. v2. improved exposition
Subjects: Group Theory (math.GR); Geometric Topology (math.GT); Rings and Algebras (math.RA)
[ total of 14 entries: 1-14 ]
[ showing up to 2000 entries per page: fewer | more ]

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