- Milnor invariants and multivariable manifold calculus of functors,
with B. Munson, in preparation.
- Configuration space integral expressions for Milnor invariants of homotopy string links,
with B. Munson, in preparation.
- Configuration space integrals and the cohomology of the space of homotopy string links,
with B. Munson, submitted (52 pages).
- Formality of the little N-discs operad,
with P. Lambrechts, submitted (101 pages).
- Cosimplicial models for spaces of links,
with B. Munson, submitted (31 pages).
- Multivariable manifold calculus of functors,
with B. Munson, to appear in Forum Mathematicum.
- Real homotopy theory of semi-algebraic sets,
with R. Hardt, P. Lambrechts, and V. Turchin, Algeb. Geom. Topol. 11 (2011), 2477-2545.
- On the cohomology of spaces of links and braids via configuration space integrals,
Sarajevo J. Math, Vol. 6 (19) (2010), 241-263.
- The rational homology of spaces of long knots in codimension >2,
with P. Lambrechts and V. Turchin, Geom. Topol. 14 (2010), 2151–2187.
- Associahedron, cyclohedron, and permutahedron as compactifications of configuration spaces,
with P. Lambrechts and V. Turchin, Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 303-332.
- Coformality and rational homotopy groups of spaces of long knots,
with G. Arone, P. Lambrechts, and V. Turchin, Math. Res. Lett., 15 (2008), no. 1, 1-14.
- Calculus of functors, operad formality, and rational homology of embedding spaces,
with G. Arone and P. Lambrechts, Acta Math., 199 (2007), no. 2, 153-198.
- A survey of Bott-Taubes integration,
J. Knot Theor. Ramif., 16 (2007), no. 1, 1-43.
- Configuration space integrals and Taylor towers for spaces of knots,
Topology Appl., 153 (2006), no. 15, 2893-2904.
- Finite type knot invariants and calculus of functors,
Compos. Math., 142 (2006), 222-250.
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- Homotopy theory of cubical diagrams,
with B. Munson, in preparation, currently at 111 pages. To be published by Cambridge University Press. The few chapters linked above are just rough drafts. Here is a tentative annotated table of contents for the entire book.
- Calculus of functors,
with G. Arone, T. Goodwillie, and B. Munson, in preparation.
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- Configuration space integrals and the cohomology of knot and link spaces
Slides from a talk given at the Configuration spaces, braids, and applications conference at Tulane University, 1/12
- Some problems arising from homotopy-theoretic methods in knot theory.
This is a partial list of literature and open problems in the study of knot and link spaces using homotopy-theoretic techniques such as manifold calculus, cosimplicial spaces, and operad actions (last updated 5/10).
- Topology and the problem of telling knots apart.
Slides from a talk given at the Wellesley Science Faculty Seminar, 2/09.
- In search of the perfect knot invariant.
Slides from a talk given at the MAA Sectional Meeting, Bentley University, 11/08.
- Manifold calculus and spaces of links.
Slides from a talk given at the AMS Sectional Meeting, Wesleyan University, 10/08.
- Calculus of functors and link invariants.
Slides from a talk given at the Third Arolla Conference on Algebraic Topology, Switzerland, 8/08.
- Kontsevich's formality of the little cubes operad and its consequences.
Notes from a talk given at the University of Oregon Basic Notions Seminar, 11/07.
- Calculus of functors, operad formality, and embedding spaces.
Notes from a talk given at the Johns Hopkins University Topology Seminar, 11/07.
- Calculus of the embedding functor and spaces of knots.
A handout for the participants in the AIM Workshop On Moduli Spaces of Knots, 1/06.
- Calculus of functors, operad formality, and embedding spaces.
Slides from a talk given at the Union College Mathematics Conference, 12/05.
- Introduction to finite type invariants.
Notes from a talk given at the University of Georgia Graduate VIGRE Seminar, 11/05.
- The rational homotopy type of spaces of knots.
Slides from a talk given at the AMS Meeting, Houston, 5/04.
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