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Geometry and Topology, ISSN 1465-3060, 08/2017, Volume 21, Issue 6, pp. 3759 - 3784
In 1976 Thurston associated to a 3-manifold N a marked polytope in H-1 (N; R), which measures the minimal complexity of surfaces representing homology classes... 
3-manifold | Novikov ring | Thurston norm | Fox calculus | MATHEMATICS | NUMBER | LOWER BOUNDS | THEOREM | GENUS | 3-MANIFOLDS | TORSION | MANIFOLDS | KNOT | ALEXANDER | CONJECTURE | Mathematics - Geometric Topology
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2019, Volume 94, Issue 1, pp. 21 - 52
Let $M$ be an oriented irreducible 3-manifold with infinite fundamental group and empty or toroidal boundary which is not $S^1 \times D^2$. Consider any... 
Topological groups, Lie groups | Global analysis, analysis on manifolds | Manifolds and cell complexes | MATHEMATICS | L-TORSION | Thurston norm | L-2-INVARIANTS | APPROXIMATION | L-2-ALEXANDER INVARIANT | TORSION | L-2-torsion | MANIFOLDS | L-2-Betti numbers | twisting with finite-dimensional representations
Journal Article
Topology and its Applications, ISSN 0166-8641, 10/2015, Volume 194, pp. 409 - 426
We explicitly construct layered-triangulations for manifolds admitting a genus-one open book decomposition with connected binding. This construction gives an... 
[formula omitted]-Thurston norm | Heegaard Floer homology | Layered-triangulations | Correction terms | Z2-Thurston norm
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 08/2019, Volume 28, Issue 9, p. 1950056
The Thurston norm of a three-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of... 
FIBER | MATHEMATICS | Thurston norm | three-manifold | one-relator groups | CONVERGENCE GROUPS
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2016, Volume 284, Issue 2, pp. 365 - 382
In 1986, W. Thurston introduced a (possibly degenerate) norm on the first cohomology group of a 3-manifold. Inspired by this definition, Turaev introduced in... 
Links | Thurston norm | Alexander polynomials | Turaev norm | TOPOLOGY | MATHEMATICS | FOLIATIONS | GRAPH MANIFOLDS | links | BOUNDARY | MINIMAL GENUS | Mathematics - Geometric Topology
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 10/2014, Volume 172, Issue 1, pp. 135 - 145
We prove that the twisted Reidemeister torsion of a 3-manifold corresponding to a fibered class is monic and we show that it gives lower bounds on the Thurston... 
Geometry | Twisted Alexander polynomial | Thurston norm | Fibered 3-manifolds | Primary 57M25 | Mathematics | Wada’s invariant | Twisted Reidemeister torsion | MATHEMATICS | Wada's invariant
Journal Article
Geometry and Topology, ISSN 1465-3060, 06/2018, Volume 22, Issue 5, pp. 2647 - 2696
We investigate Friedl and Luck's universal L-2-torsion for descending HNN extensions of finitely generated free groups, and so in particular for F-n-by-Z... 
Alexander norm | Ascending HNN extensions of free groups | BNS invariants | Thurston norm | Free-by-cyclic groups | MATHEMATICS | 3-MANIFOLDS | FINITE | GROUP-RINGS
Journal Article
by Ni, Yi
Geometry and Topology, ISSN 1364-0380, 2009, Volume 13, Issue 5, pp. 2991 - 3019
We prove that, for a link L in a rational homology 3-sphere, the link Floer homology detects the Thurston norm of its complement. This result has been proved... 
Rational homology 3-sphere | Thurston norm | Taut foliation | Link | Link Floer homology | TOPOLOGY | MATHEMATICS | FOLIATIONS | INVARIANTS | GENUS | 3-MANIFOLDS | HOLOMORPHIC DISKS | Mathematics - Geometric Topology
Journal Article
Geometry and Topology, ISSN 1364-0380, 2009, Volume 13, Issue 3, pp. 1313 - 1336
Let F = pi(1) (S) where S is a compact, connected, oriented surface with chi(S) < 0 and nonempty boundary. (1) The projective class of the chain partial... 
Hyperbolic structure | Polyhedral norm | Rotation number | Bounded cohomology | Immersion | Rigidity | Free group | Scl | Surface | MATHEMATICS | THURSTON NORM | SUBGROUPS | HOMOLOGY
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 01/2009, Volume 239, Issue 1, pp. 1 - 15
Given a triangulation of a closed, oriented, irreducible, atoroidal 3-manifold every oriented, incompressible surface may be isotoped into normal position... 
3-manifold | Triangulation | Thurston norm | Normal surface | MATHEMATICS | 3-MANIFOLDS | triangulation | normal surface
Journal Article
Topology, ISSN 0040-9383, 2006, Volume 45, Issue 6, pp. 929 - 953
Every element in the first cohomology group of a 3-manifold is dual to embedded surfaces. The Thurston norm measures the minimal ‘complexity’ of such surfaces.... 
3-manifolds | Twisted Alexander polynomials | Knot genus | Thurston norm | Fibered knots | REIDEMEISTER TORSION | MATHEMATICS | knot genus | COHOMOLOGY | FOLIATIONS | INVARIANTS | twisted Alexander polynomials | HOMOLOGY | KNOTS | fibered knots
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2007, Volume 230, Issue 2, pp. 271 - 296
Cochran introduced Alexander polynomials over noncommutative Laurent polynomial rings. Their degrees were studied by Cochran, Harvey and Turaev, who gave lower... 
3-manifolds | Knot genus | Reidemeister torsion | Thurston norm | MATHEMATICS | knot genus | REPRESENTATIONS | ALEXANDER
Journal Article
International Journal of Computer Mathematics: Computer Systems Theory, ISSN 2379-9927, 01/2020, Volume 5, Issue 1, pp. 15 - 24
We discuss some applications of 3-manifold topology to cryptography. In particular, we propose a public-key and a symmetric-key cryptographic scheme based on... 
3-manifold | cryptography | Thurston norm | public key | Hyperbolic
Journal Article
Topology, ISSN 0040-9383, 2005, Volume 44, Issue 5, pp. 895 - 945
We define an infinite sequence of new invariants, δ n , of a group G that measure the size of the successive quotients of the derived series of G. In the case... 
Alexander norm | Derived series | Thurston norm | TOPOLOGY | SURGERY | MATHEMATICS | FOLIATIONS | derived series
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2012, Volume 259, Issue 2, pp. 373 - 385
We compare the l(1)-seminorm parallel to.parallel to(1) and the manifold seminorm parallel to.parallel to(man) on n-dimensional integral homology classes.... 
Tomei manifold | Singular homology | Manifold norm | Thurston norm | Steenrod's realization problem | L | Simplicial volume | norm | MATHEMATICS | l-norm | ASPHERICAL MANIFOLDS | singular homology | simplicial volume | manifold norm | Differential Geometry | Mathematics
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 2007, Volume 7, Issue 1, pp. 755 - 777
Given a 3-manifold the second author defined functions delta(n): H-1(M; Z) -> N, generalizing McMullen's Alexander norm, which give lower bounds on the... 
3-manifolds | Alexander norm | Dieudonné | Thurston norm | Determinant | MATHEMATICS | 3-MANIFOLDS | INVARIANTS
Journal Article
Geometry and Topology, ISSN 1465-3060, 2004, Volume 8, pp. 311 - 334
Journal Article
GEOMETRY & TOPOLOGY, ISSN 1364-0380, 2004, Volume 8, Issue 1, pp. 311 - 334
We prove that, like the Seiberg-Witten monopole homology, the Heegaard Floer homology for a three-manifold determines its Thurston norm. As a consequence, we... 
TOPOLOGY | MATHEMATICS | Thurston norm | Dehn surgery | Floer homology | FOLIATIONS | INVARIANTS | Seifert genus | 3-MANIFOLDS | NORM | 4-MANIFOLDS | contact structures
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2017, Volume 19, Issue 12, pp. 3867 - 3910
The Teichmuller polynomial of a fibered 3-manifold, introduced in [McM00], plays a useful role in the construction of mapping classes having a small stretch... 
Pseudo-Anosov homeomorphism | Teichmüller polynomial | Thurston norm | pseudo-Anosov homeomorphism | MATHEMATICS, APPLIED | FOLIATIONS | INVARIANTS | Teichmuller polynomial | SMALL DILATATION | PSEUDO-ANOSOV BRAIDS | MATHEMATICS | SURFACE HOMEOMORPHISMS | SMALL ENTROPY | NORM | MAGIC 3-MANIFOLD
Journal Article
by Ni, Y and Wu, ZT
TOPOLOGY AND ITS APPLICATIONS, ISSN 0166-8641, 10/2015, Volume 194, pp. 409 - 426
We explicitly construct layered-triangulations for manifolds admitting a genus-one open book decomposition with connected binding. This construction gives an... 
MATHEMATICS, APPLIED | RATIONAL GENUS | INVARIANTS | Heegaard Floer homology | HOLOMORPHIC DISKS | Correction terms | Z-Thurston norm | FLOER HOMOLOGY | MATHEMATICS | BOUNDS | 3-MANIFOLDS | 4-MANIFOLDS | Layered-triangulations | SURFACES
Journal Article
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