De Rham model for string topology

By S. Merkulov. 2003

48 citations recorded by the source corpus.

Using the theory of iterated integrals, we give new short proofs of some of the main theorems of string topology including the one which relates Chas-Sullivan algebra structure on the homology of the free loop space of a simply connected closed oriented manifold to the Hochschild cohomology of the de Rham algebra.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a9f054dbd599262353c3e3d5f47b037af4595cfe

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Thomas Tradler
2. Y. Félix
3. Micheline Vigué-Poirrier
4. Jean-Claude Thomas
5. R. Kaufmann
6. K. Costello
7. Luc Menichi

In Geometry and Topology

1. Y. Félix
2. R. Kaufmann
3. Thomas Tradler
4. Jean-Claude Thomas
5. Luc Menichi
6. K. Costello

In Mathematical Physics

1. Y. Félix
2. R. Kaufmann
3. Thomas Tradler
4. Micheline Vigué-Poirrier
5. Jean-Claude Thomas
6. Luc Menichi
7. K. Costello

Citations in the corpus

• A proof of a cyclic version of Deligne’s conjecture via Cacti (2004, methodology): “ products of associahedra and cyclohedra and are indexed by trees of the type appearing in [KS]. Finally using the cyclic description of the free loop space or the iterated integral representation of [Me] together with the results mentioned above, we expect to be able to obtain an action of the (dec”
• Rational string topology (2004, background): “Merkulov, [15], gives a proof based on the theory of iterated integrals when the coefficients are the real numbers.”
• Batalin-Vilkovisky algebra structures on Hochschild Cohomology (2007, unknown): “Over the reals or over the rationals, two proofs of such an isomorphism of graded algebras have been given by Merkulov [25] and Félix, Thomas, Vigué-Poirrier [14].”
• The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products (2008, methodology): “In fact, it has been shown by Felix-Thomas [6] and Merkulov [17], that in characteristic zero, the BValgebras on H•(A,A) and H•(LX) do coincide.”
• Algebraic models in geometry (2008, unknown): “ωk ∧ π∗ 1 (ωk+1) on Pfree(M) can also be presented as integrals along a fiber, see [105] or [191].”