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Graph manifolds, left-orderability and amalgamation

- Adam Clay, Tye Lidman, Liam Watson
- Mathematics
- 2 June 2011

We show that every irreducible toroidal integer homology sphere graph manifold has a left-orderable fundamental group. This is established by way of a specialization of a result due to Bludov and… Expand

32 5- PDF

Surgery obstructions and Heegaard Floer homology

- J. Hom, Cagri Karakurt, Tye Lidman
- Mathematics
- 7 August 2014

Using Taubes' periodic ends theorem, Auckly gave examples of toroidal and hyperbolic irreducible integer homology spheres which are not surgery on a knot in the three-sphere. We give an obstruction… Expand

16 2- PDF

Ribbon homology cobordisms

- A. Daemi, Tye Lidman, David Shea Vela-Vick, C. M. Wong
- Mathematics
- 22 April 2019

We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. Using… Expand

8 2

Rank inequalities for the Heegaard Floer homology of Seifert homology spheres

- Cagri Karakurt, Tye Lidman
- Mathematics
- 2 October 2013

We establish three rank inequalities for the reduced flavor of Heegaard Floer homology of Seifert fibered integral homology spheres. Combining these inequalities with the known classifications of… Expand

11 2- PDF

APPLICATIONS OF INVOLUTIVE HEEGAARD FLOER HOMOLOGY

- Kristen Hendricks, J. Hom, Tye Lidman
- Mathematics
- Journal of the Institute of Mathematics of…
- 6 February 2018

Abstract We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere… Expand

12 2- PDF

Framed instanton homology of surgeries on L-space knots

- Tye Lidman, Juanita Pinz'on-Caicedo, C. Scaduto
- Mathematics
- 6 March 2020

An important class of three-manifolds are L-spaces, which are rational homology spheres with the smallest possible Floer homology. For knots with an instanton L-space surgery, we compute the framed… Expand

8 2- PDF

The equivalence of two Seiberg-Witten Floer homologies

- Tye Lidman, C. Manolescu
- Mathematics
- 2 March 2016

We show that monopole Floer homology (as defined by Kronheimer and Mrowka) is isomorphic to the S^1-equivariant homology of the Seiberg-Witten Floer spectrum constructed by the second author.

14 1- PDF

Berge-Gabai knots and L-space satellite operations

- J. Hom, Tye Lidman, F. Vafaee
- Mathematics
- 6 June 2014

Let P(K) be a satellite knot where the pattern P is a Berge–Gabai knot (ie a knot in the solid torus with a nontrivial solid torus Dehn surgery) and the companion K is a nontrivial knot in S^3. We… Expand

12 1- PDF

Cosmetic surgery in L-spaces and nugatory crossings

- Tye Lidman, Allison H. Moore
- Mathematics
- 2 July 2015

The cosmetic crossing conjecture (also known as the “nugatory crossing conjecture”) asserts that the only crossing changes that preserve the oriented isotopy class of a knot in the 3-sphere are… Expand

10 1- PDF

Quasi-alternating links with small determinant

- Tye Lidman, Steven Sivek
- Mathematics
- Mathematical Proceedings of the Cambridge…
- 16 July 2015

Abstract Quasi-alternating links of determinant 1, 2, 3 and 5 were previously classified by Greene and Teragaito, who showed that the only such links are two-bridge. In this paper, we extend this… Expand

5 1- PDF

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