On variations of s-invariants from sl3-link homology, preprint. pdf.
On the Khovanov homology of 3-braids, preprint. pdf.
Local equivalence and refinements of Rasmussen's s-invariant, preprint, with N. Dunfield and R. Lipshitz. pdf.
Two second Steenrod squares for odd Khovanov homology, preprint. pdf.
Recent Publications:
A note on the X-torsion order of a knot, preprint, to appear in Canad. Math. Bull. The original publication is available here. pdf.
On an integral version of the Rasmussen invariant, Michigan Math. J. 75 (2025), 65-88. The original publication is available here. pdf.
A calculus for flow categories, with A. Lobb and P. Orson, Adv. Math. 409 B (2022), 108665, 58pp. The original publication is available here. pdf.
A scanning algorithm for odd Khovanov homology, Algebr. Geom. Topol. 22 (2022), 1287-1324. The original publication is available here. pdf. Additional material.
A fast algorithm for calculating s-invariants, Glasg. Math. J. 63 (2021), 378-399. The original publication is available here and a corrigendum here. pdf. Additional material.
Arbitrarily large torsion in Khovanov cohomology, with S. Mukherjee, Quantum Top. 12 (2021), 243-264. The original publication is available here. pdf.
Torsion calculations in Khovanov cohomology, J. Knot Theory Ramifications 29 (2020), 2071001, 7pp. The original publication is available here. pdf. Additional material.
Khovanov homotopy calculations using flow category calculus, with A. Lobb and P. Orson, Exp. Math. 29 (2020), 475-500. The original publication is available here. pdf. Additional material.
An sln stable homotopy type for matched diagrams, with D. Jones and A. Lobb, Adv. Math. 356 (2019), 106816, 70pp. The original publication is available here. pdf. Additional material.
Framed cobordism and flow category moves, with A. Lobb and P. Orson, Algebr. Geom. Topol. 18 (2018), 2821-2858. The original publication is available here. pdf.
Morse moves in flow categories, with D. Jones and A. Lobb, Indiana Univ. Math. J. 66 (2017), 1603-1657. The original publication is available here. pdf.
A Khovanov stable homotopy type for colored links, with A. Lobb and P. Orson, Algebr. Geom. Topol. 17 (2017), 1261-1281. The original publication is available here. pdf. Additional material.
Intersection homology of linkage spaces in odd dimensional Euclidean space, Algebr. Geom. Topol. 16 (2016), 483-508. The original publication is available here. pdf
Intersection homology of linkage spaces, J. Topol. Anal. 8 (2016), 25-58. The original publication is available here. pdf
On singular foliations on the solid torus, with J.L. Arraut and L.F. Martins, Topology Appl. 160 (2013), 1659-1674. The original publication is available here. pdf
Homology of moduli spaces of linkages in high-dimensional euclidean space, Algebr. Geom. Topol. 13 (2013), 1183-1224. The original publication is available here. pdf
The Walker conjecture for chains in Rd, with M. Farber and J.-Cl. Hausmann, Math. Proc. Cambridge Philos. Soc. 151 (2011), 283-292. The original publication is available here. pdf
On the relative Lusternik-Schnirelmann category with respect to a real cohomology class, with Tieqiang Li, Glasg. Math. J. 53 (2011), 169-183. The original publication is available here. pdf
The isomorphism problem for planar polygon spaces, J. Topol. 3 (2010), 713-742. The original publication is available here. pdf
Closed 1-forms in topology and geometric group theory, with M. Farber and R. Geoghegan, Uspekhi Mat. Nauk 65 (2010), 145-176; translation in Russian Math. Surveys 65 (2010), 143-172. The original publication is available here. pdf
Novikov homology of HNN-extensions and right-angled Artin groups, Algebr. Geom. Topol. 9 (2009), 773-809. The original publication is available
here. pdf
Closed 1-forms in topology and dynamics, with M. Farber, Uspekhi Mat. Nauk 63:6 (2008), 91-156; translation in Russian Math. Surveys 63 (2008) 1079-1136. The original publication is available here. pdf
On the direct product conjecture for sigma invariants, Bull. Lond. Math. Soc. 40 (2008), 675-684. The original publication is available here. pdf
Homological category weights and estimates for cat1(X,ξ), with M. Farber, J. Eur. Math. Soc. 10 (2008), 243-266. The original publication is available here. pdf
Homology of planar polygon spaces, with M. Farber, Geom. Dedicata 125 (2007), 75-92. The original publication is available at www.springerlink.com. pdf
Cohomological estimates for cat(X,ξ), with M. Farber, Geom. Topol. 11 (2007), 1255-1288. The original publication is available here. pdf
On the Whitehead group of Novikov rings associated to irrational homomorphisms, J. Pure Appl. Algebra 208 (2007) 449-466. The original publication is available here.
pdf
Moving homology classes to infinity, with M. Farber, Forum Math. 19 (2007), 281-296. The original publication is available here. pdf
Novikov-Betti numbers and the fundamental group, with M. Farber, Uspekhi Mat. Nauk 61:6 (2006), 193-194; translation in Russian Math. Surveys 61 (2006) 1173-1175. The original publication is available here or here. pdf
Closed 1-forms with at most one zero, with M. Farber, Topology 45 (2006), 465-473. The original publication is available
here.
pdf
Finite domination, Novikov homology and nonsingular closed 1-forms, Math. Z. 252 (2006), 623-654. The original publication is available at www.springerlink.com. pdf
On the algebraic K- and L-theory of word hyperbolic groups, with D. Rosenthal, Math. Ann. 332 (2005), 523-532. The original publication is available at www.springerlink.com.
pdf
Zeta functions for gradients of closed 1-forms, Topology Appl. 144 (2004), 147-160. The original publication is available
here. pdf
On the Lusternik-Schnirelman theory of a real cohomology class, Manuscripta Math. 113 (2004), 85-106. The original publication is available at www.springerlink.com. pdf
Geometric chain homotopy equivalences between Novikov complexes, High-dimensional manifold topology, 469-498, World Sci. Publishing, River Edge, NJ, 2003. pdf
Controlled connectivity of closed 1-forms, Algebr. Geom. Topol. 2 (2002), 171-217. The original publication is available
here. pdf
One-parameter fixed-point theory and gradient flows of closed 1-forms, K-Theory 25 (2002), 59-97. The original publication is available here. pdf
Gradient flows of closed 1-forms and their closed orbits, Forum Math. 14 (2002), 509-537. The original publication is available
here. pdf
Obstructions to homotopy invariance in parametrized fixed point theory, with R. Geoghegan and A. Nicas, Geometry and topology: Aarhus (1998), 157-175, Contemp. Math. 258, Amer. Math. Soc., Providence, RI, 2000.
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