**Research Monographs:**

2. The
equivalence of two Seiberg-Witten Floer homologies (with T. Lidman),
*Astérisque*, Vol. 399 (2018)

1. Cornered
Heegaard Floer homology (with C. Douglas and R. Lipshitz), *Memoirs
of the American Mathematical Society*, to appear

**Research Articles:**

26. A sheaf-theoretic SL(2,C) Floer homology for knots (with L. Côté), preprint (2018)

25. The Knight Move Conjecture is false (with M. Marengon), preprint (2018)

24. A sheaf-theoretic
model for SL(2,C) Floer homology (with M. Abouzaid), *Journal
of the European Mathematical Society*, to appear

23. Involutive Heegaard
Floer homology and plumbed three-manifolds (with I. Dai), *Journal
of the Institute of Mathematics of Jussieu*, to appear

22. A connected sum
formula for involutive Heegaard Floer homology (with K. Hendricks and I.
Zemke), *Selecta Mathematica*, Vol. 24 (2018), 1183-1245

21. Floer
homology and covering spaces (with T. Lidman), *Geometry &
Topology*, Vol. 22 (2018), 2817-2838

20. Involutive Heegaard
Floer
homology (with K. Hendricks), *Duke Mathematical Journal*, Vol.
166 (2017), 1211-1299

19. On the intersection
forms of spin four-manifolds with boundary, *Mathematische
Annalen*, Vol. 359 (2014), 695-728

18. A generalized asynchronous
computability theorem (with E. Gafni and P. Kuznetsov), in *Proceedings
of the 2014 ACM Symposium on Principles of Distributed Computing* (PODC
'14), ACM, New York (2014), 222-231

17. Pin(2)-equivariant
Seiberg-Witten Floer homology and the Triangulation Conjecture,
*Journal of the American Mathematical Society*, Vol. 29 (2016),
147-176

16. An untwisted
cube of resolutions for knot Floer homology, *Quantum Topology*,
Vol. 5 (2014), 185-223

15. On the
algebra of cornered Floer homology (with C. Douglas), *Journal of
Topology*,
Vol. 7 (2014), 1-68

14. Heegaard Floer homology and integer surgeries on links (with P. Ozsváth), preprint (2010, revised 2017)

13. Grid diagrams and Heegaard Floer invariants (with P. Ozsváth and D. Thurston), preprint (2009, revised 2017)

12. Floer homology on
the
extended moduli space (with C. Woodward), in *Perspectives
in Analysis, Geometry and Topology*, Progress in Mathematics
Vol. 296, Birkhauser/Springer, New York (2012), 283-329

11. On the
Khovanov and knot Floer homologies of quasi-alternating links (with P.
Ozsváth), in *Proceedings of the Gökova Geometry-Topology
Conference 2007*, Gökova (2008), 60-81

10. Combinatorial
cobordism maps in hat Heegaard Floer theory (with R. Lipshitz and J.
Wang), *Duke Mathematical Journal*, Vol. 145 (2008), 207-247

9. On
combinatorial link Floer homology (with P.
Ozsváth, D. Thurston and Z. Szabó), *Geometry & Topology*,
Vol. 12 (2007), 2339-2412

8. An
unoriented skein exact triangle for knot Floer homology,
*Mathematical Research Letters*, Vol. 14 (2007), 839-852

7. A
combinatorial description of knot Floer homology (with P.
Ozsváth and S. Sarkar), *Annals of Mathematics*, Vol. 169 (2009),
633-660

6. Link homology
theories from symplectic geometry, *Advances in Mathematics*,
Vol. 211 (2007), 363-416

5. A
concordance
invariant from the Floer homology of double branched covers (with B.
Owens), *International Mathematics Research Notices*, Vol. 2007, doi:10.1093/imrn/rnm077

4. Nilpotent slices,
Hilbert schemes, and the Jones polynomial, *Duke Mathematical
Journal*, Vol. 132 (2006), 311-369

3. A gluing
theorem for the relative Bauer-Furuta invariants, *Journal of
Differential Geometry*, Vol. 76 (2007), 117-153

2. Periodic Floer pro-spectra from the Seiberg-Witten equations (with P. Kronheimer), unpublished manuscript (2003)

1. Seiberg-Witten-Floer
stable homotopy type of three-manifolds with b_1=0, *Geometry &
Topology*, Vol. 7 (2003), 889-932 (with Errata)

**Expository Articles:**

7. Homology cobordism
and
triangulations, to appear in *Proceedings of the International Congress
of Mathematicians, Rio de Janeiro, 2018*

6. Lectures on
the triangulation conjecture, in *Proceedings of the Gökova
Geometry / Topology Conference 2015*, Gökova (2016), 1-38

5. Floer theory and
its topological
applications, *Japanese Journal of Mathematics*, Vol. 10 (2015),
105-133

4. Triangulations of manifolds,
*Notices of the International Congress of Chinese Mathematicians*, Vol. 2 (2014), no.2, 21-23

3. An introduction to
knot Floer homology, in *Physics and mathematics of link homology*, Contemp.
Math., Vol. 680, AMS (2016), 99-135

2. The Conley
index, gauge theory, and triangulations, *Journal of Fixed Point Theory and
Applications*, Vol. 13 (2013), 431-457

1. Grid
diagrams in Heegaard Floer theory, in *European Congress of Mathematics,
Krakow, 2-7 July, 2012*, European Mathematical Society (2013), 643-657