Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32579
Topological Quantum Diffeomorphisms in Field Theory and the Spectrum of the Space-Time

Authors: Francisco Bulnes


Through the Fukaya conjecture and the wrapped Floer cohomology, the correspondences between paths in a loop space and states of a wrapping space of states in a Hamiltonian space (the ramification of field in this case is the connection to the operator that goes from TM to T*M) are demonstrated where these last states are corresponding to bosonic extensions of a spectrum of the space-time or direct image of the functor Spec, on space-time. This establishes a distinguished diffeomorphism defined by the mapping from the corresponding loops space to wrapping category of the Floer cohomology complex which furthermore relates in certain proportion D-branes (certain D-modules) with strings. This also gives to place to certain conjecture that establishes equivalences between moduli spaces that can be consigned in a moduli identity taking as space-time the Hitchin moduli space on G, whose dual can be expressed by a factor of a bosonic moduli spaces.

Keywords: Floer cohomology, Fukaya conjecture, Lagrangian submanifolds, spectrum of ring, topological quantum diffeomorphisms.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 911


[1] F. Bulnes, “Integral Geometry Methods in the Geometrical Langlands Program”, SCIRP, USA, 2016.
[2] F. Bulnes, “Geometrical Langlands Ramifications and Differential Operators Classification by Coherent D-Modules in Field Theory,” Journal of Mathematics and System Science, 3, no. 10, 2013, USA, pp491-507.
[3] Bulnes, F. (2014) Derived Categories in Langlands Geometrical Ramifications: Approaching by Penrose Transforms. Advances in Pure Mathematics, 4, 253-260. doi: 10.4236/apm.2014.46034.
[4] J. Milnor, “On spaces having the homotopy type of a CW-complex” Trans. Amer. Math. Soc. 90 (1959), 272–280.
[5] F.Bulnes, Penrose Transform on D-Modules, Moduli Spaces and Field Theory, Advances in Pure Mathematics, 2012, 2(6), pp. 379-390.
[6] M. Ramírez, L. Ramírez, O. Ramírez, F. Bulnes, “Field Ramifications: The Energy-Vacuum Interaction that Produces Movement,” Journal on Photonics and Spintronics, Vol. 2, no. 3, USA, 2013, pp4-11.
[7] F. Bulnes (2013). Quantum Intentionality and Determination of Realities in the Space-Time Through Path Integrals and Their Integral Transforms, Advances in Quantum Mechanics, Prof. Paul Bracken (Ed.), ISBN: 978-953-51-1089-7, InTech, DOI: 10.5772/53439. Published from 03/04/2013:
[8] K. Fukaya, Floer Homology and Mirror Symmetry I, Department of Mathematics, Faculty of Science, Kyoto University, Kitashirakawa, Kyoto, 606-8224, Japan.
[9] A. Abbondandolo, M. Schwarz, “Floer homology of cotangent bundle and the loop product,” Geom. Top. 14 (2010), no. 3, 1569-1722.
[10] A. Kapustin, M. Kreuser and K. G. Schlesinger, Homological mirror symmetry: New Developments and Perspectives, Springer. Berlin, Heidelberg, 2009.
[11] D. Eisenbud: J. Harris (1998). The Geometry of Schemes. Springer-Verlag, USA.
[12] I. Verkelov, Commutative Schemes of Rings and Koszul Dualities to Integral Geometry, Journal of Mathematics, Vol. 1 Issue 1, pp. 1-5.
[13] F. Bulnes, Integral Geometry Methods on Derived Categories in Field Theory II, Pure and Applied Mathematics Journal, Special Issue: Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program, 2014, 3(6-2), pp. 1-5.
[14] Blumenhagen, Ralph; Lüst, Dieter; Theisen, Stefan (2012), Basic Concepts of String Theory, Theoretical and Mathematical Physics, Springer, p. 487, "Orbifolds can be viewed as singular limits of smooth Calabi–Yau manifolds".
[15] N. Hitchin (2003), "Generalized Calabi–Yau manifolds", The Quarterly Journal of Mathematics 54 (3): 281–308.
[16] F. Bulnes, “Integral geometry methods on deformed categories to geometrical Langlands ramifications in field theory,” Ilirias Journal of Mathematics, Vol 3, Issue 1 (2014) pp. 1-13.
[17] R. M. Switzer, Homotopy and Homology. Springer, 2nd Edition, 1975.