Research

My main research interests are in topology and geometry, including low-dimensional topology, knot theory, Floer theory, gauge theory, symplectic/contact topology, and orderability of groups.   My research is currently supported by the National Science Foundation and was previously supported by the Sloan Foundation.

Collaborators:

Paolo Aceto (Université de Lille), Santana Afton (Georgia Tech), Dave Auckly (KSU), John Baldwin (Boston College), Inanc Baykur (U Mass), Roger Casals (UC Davis), Adam Clay (U Manitoba), Ali Daemi (Wash U), Nate Dowlin, Steve Evans (Berkeley), Mike Freedman (Harvard/UCSB), Cameron Gordon (UT Austin), Eugene Gorsky (UC Davis), Jonathan Hanselman (Princeton), Kristen Hendricks (Rutgers), Jen Hom (Georgia Tech), Cagri Karakurt (Bogazici), Miriam Kuzbary (Amherst), Sudipta Kolay (Brown), Artem Kotelskiy (Stony Brook), Slava Krushkal (UVA), Cagatay Kutluhan (Buffalo), Adam Levine (Duke), Robert Lipshitz (Oregon), Beibei Liu (Ohio State), Ciprian Manolescu (Stanford), Allison Miller (Swarthmore), Mike Miller Eismeier (U Vermont), Allison Moore (Virginia Commonwealth), JungHwan Park (KAIST), Lisa Piccirillo (MIT/UT Austin), Juanita Pinzon-Caicedo (Notre Dame), Radmila Sazdanovic (NCSU), Steven Sivek (Imperial), Chris Scaduto (U Miami), Eamonn Tweedy (Widener), Fery Vafaee (Google), Mariel Vazquez (UC Davis), Shea Vela-Vick (LSU), Josh Wang (MIT), Liam Watson (UBC), Mike Wong (Ottawa), Raphael Zentner (Durham), Claudius Zibrowius (Durham), Daniele Zuddas (Trieste), Nick Zufelt (Phillips Andover)

Preprints and papers to appear:

M. Freedman, S. Krushkal, T. Lidman.  Spineless 5-manifolds and the deformation conjecture.  Available at arXiv:2401.03498.

T. Lidman and A.H. Moore.  Adjacency of three-manifolds and Brunnian links.  Available at arXiv:2308.06211.

A.S. Levine, T. Lidman, L. Piccirillo.  New constructions and invariants of closed exotic four-manifolds.  Available at arXiv:2307.08130.

P. Aceto, A. Daemi, J. Hom, T. Lidman, J. Park.  Handle decomposition complexity and representation spaces.  Available at arXiv:2210.06607.

T. Lidman, A. Miller, J. Pinzon-Caicedo.  Linking number obstructions to satellite homomorphisms.  Available at arXiv:2207.14198.

A. Daemi, T. Lidman, M. Miller Eismeier.  3-manifolds without any embedding in symplectic 4-manifolds. To appear in Geom. and Topol. Available at arXiv:2207.03631.  

J. Hom, T. Lidman, J. Park.  Unknotting number and cabling.  Available at arXiv:2206.04196.

A. Kotelskiy, T. Lidman, A.H. Moore, L. Watson, C. Zibrowius.  Cosmetic operations and Khovanov multicurves.  To appear in Math. Annalen.  Available at arXiv:2109.14049.

T. Lidman. Cosmetic surgeries and the Poincare homology sphere. Available at arXiv:1902.06801. 

T. Lidman. Heegaard Floer homology and triple cup products. Available at arXiv:1011.4277.

T. Lidman. Framed Floer homology. Available at arXiv:1109.3756. 

Publications:

T. Lidman, J. Pinzon-Caicedo, R. Zentner.  Toroidal homology spheres and SU(2)-representations.  J. Topol. 16 (2023), no. 1, 344-367.

E. Gorsky, T. Lidman, B. Liu, A.H. Moore. Triple linking numbers and Heegaard Floer homology.  Int. Math. Res. Not. IMRN (2023), no. 6, 4501-4554.

J. Hom and T. Lidman. Dehn surgery and non-separating two-spheres.  Open Book Ser., 5 Mathematical Sciences Publishers, 2022, 145-153.

D. Auckly, R.I. Baykur, R. Casals, S. Kolay, T. Lidman, D. Zuddas.  Branched covering simply-connected 4-manifolds.  Open Book Ser., 5 Mathematical Sciences Publishers, 2022, 31-42.

T. Lidman and A.H. Moore and C. Zibrowius. L-space knots have no essential Conway spheres.  Geom. Topol.  26 (2022), no. 5, 2065-2102.  

J. Hom, A. Levine, and T. Lidman. Knot concordance in homology cobordisms. Duke Math. J. 171 (2022), no. 15, 3089-3131.

A. Daemi, T. Lidman, D.S. Vela-Vick, C.-M. Michael Wong. Obstructions to ribbon homology cobordisms. Adv. Math.  408 (2022).

T. Lidman, J. Pinzon-Caicedo, C. Scaduto. Framed instanton homology of surgeries on L-space knots.  Indiana Univ. Math J. 71 (2022), no. 3, 1317-1347.

K. Hendricks, T. Lidman, R. Lipshitz. Rank inequalities for the Heegaard Floer homology of branched covers.  Doc. Math. 27 (2022), 581-612.

J.A. Baldwin, T. Lidman, C.-M. Michael Wong. Lagrangian cobordisms and Legendrian invariants in knot Floer homology. Mich. Math. J. 71 (2022), no. 1, 145-175.

J.A. Baldwin, N. Dowlin, A.S. Levine, T. Lidman, R. Sazdanovic. Khovanov homology detects the figure-eight knot. Bull. Lond. Math. Soc. 53 (2021), no. 3, 871-876.

C. Karakurt, T. Lidman, and E. Tweedy. Heegaard Floer homology and splicing homology spheres.  Math. Res. Lett. 28 (2021), no. 1, 93-106.

K. Hendricks, J. Hom, and T. Lidman. Applications of involutive Heegaard Floer homology.  J. Inst. Math. Jussieu 20 (2021), no. 1, 187-224.

T. Lidman, A.H. Moore, and M. Vazquez. Distance one lens space fillings and band surgery on the trefoil knot. Algebr. Geom. Topol. 19 (2019), no. 5, 2439-2484.

A. Levine and T. Lidman. Simply-connected spineless 4-manifolds. Forum Math. Sigma 7 (2019), e14, 11pp.

J. Hanselman, C. Kutluhan, and T. Lidman. A remark on the geography problem in Heegaard Floer homology. Proc. of Symp. in Pure Math. (102), 103-111, 2019.

T. Lidman and C. Manolescu. Floer homology and covering spaces. Geom. Topol., 22 (2018) 2817-2838.

T. Lidman and C. Manolescu. The equivalence of two Seiberg-Witten Floer homologies. Asterisque, 399 (2018).

J. Hom and T. Lidman. A note on surgery obstructions and hyperbolic integer homology spheres. Proc. Amer. Math. Soc., 146 (2018), no. 3, 1363-1365.

T. Lidman and E. Tweedy. A note on concordance properties of bers in Seifert homology spheres. Can. Math. Bull. 61 (2018), no.4, 754-767.

C. Gordon and T. Lidman. Knot contact homology detects cabled, composite, and torus knots. Proc. Amer. Math. Soc. 145 (2017), no. 12, 5405-5412.

C. Gordon and T. Lidman. Corrigendum to "Taut foliations, left-orderability, and cyclic branched covers". Acta Math. Vietnam. 42 (2017), no. 4, 775-776.

T. Lidman and S. Sivek. Quasi-alternating links with small determinant. Math. Proc. Cambridge., 162 (2017), no. 2, 319-336.

J. Hom, T. Lidman, and L. Watson. The Alexander invariant, Seifert forms, and categorification. J. Topology, 10, (2017), 22-100.

T. Lidman and A.H. Moore. Cosmetic surgeries in L-spaces and nugatory crossings. Trans. Amer. Math. Soc., 369 (2017), no. 5, 3639-3654.

J. Hom and T. Lidman. A note on positive denite symplectic four-manifolds. J. Eur. Math. Soc. 21 (2019), no.1, 257-270.

J. Hom, C. Karakurt, and T. Lidman. Surgery obstructions and Heegaard Floer homology. Geom. Topol., 20 (2016) 2219-2251.

T. Lidman and S. Sivek. Contact structures and reducible surgeries. Compos. Math., 152 (2016), no. 1, 152-186.

T. Lidman and A.H. Moore. Pretzel knots with L-space surgeries. Mich. Math. J., 65 (2016), no. 1, 105-130.

J. Hom, T. Lidman, and N. Zufelt. Reducible surgeries and Heegaard Floer homology. Math. Res. Lett., 22 (2015), no. 3, 763-788.

C. Karakurt and T. Lidman. Rank inequalities for the Heegaard Floer homology of Seifert homology spheres. Trans. Amer. Math. Soc., 367 (2015), 7291-7322.

J. Hom, T. Lidman, and F. Vafaee. Berge-Gabai knots and L-space satellite operations. Algebr. Geom. Topol., 14 (2014), no. 6, 3745-3763.

C. Gordon and T. Lidman. Taut foliations, left-orderability, and cyclic branched covers. Acta Math. Vietnam., 39 (2014), no. 4, 599-635.

T. Lidman and L. Watson. Non-fibered L-space knots. Pacific J. Math., 267 (2014), no. 2, 423-429.

T. Lidman. On the infinity flavor of Heegaard Floer homology and the integral cohomology ring. Comment. Math. Helv., 88 (2013), no. 4, 875-898.

A. Clay, T. Lidman, and L. Watson. Graph manifolds, left-orderability and amalgamation. Algebr. Geom. Topol., 13 (2013), no. 4, 2347-2368.

S. Evans and T. Lidman. Asymptotic evolution of acyclic random mappings. Electron. J. Probab. 12 (2007), 1051-1180.

S. Evans and T. Lidman. Expectation, conditional expectation and martingales in local fields. Electron. J. Probab. 12 (2007), 498-515.