We define the Brownian motion on a torus group. We define the stochastic integral of a one-form o... more We define the Brownian motion on a torus group. We define the stochastic integral of a one-form over each canonical cycle of the torus and the stochastic integral on a two-form over the torus. We cannot apply martingale theory in order to define these stochastic integrals. We define a stochastic cohomology in the Chen–Souriau sense of the torus group, which
We define stochastic pants, and the stochastic parallel transport over them for the Felder–Gawedz... more We define stochastic pants, and the stochastic parallel transport over them for the Felder–Gawedzki–Kupiainen line bundle over the loop space. It is related to the construction of stochastic integrals, where we cannot use martingale theory in order to define them. We get a stochastic fusion of the two line bundles when the two loops meet.
We give the definition of a line bundle over the Brownian bridge by using its section. This allow... more We give the definition of a line bundle over the Brownian bridge by using its section. This allows us to define a Hilbert space of sections of a line bundle over the Brownian bridge associated to the transgression of a representative of an element of H3(M;Z). We consider the case of a string structure over the Brownian bridge: this allows
We define the Brownian motion on a torus group. We define the stochastic integral of a one-form o... more We define the Brownian motion on a torus group. We define the stochastic integral of a one-form over each canonical cycle of the torus and the stochastic integral on a two-form over the torus. We cannot apply martingale theory in order to define these stochastic integrals. We define a stochastic cohomology in the Chen–Souriau sense of the torus group, which
We define stochastic pants, and the stochastic parallel transport over them for the Felder–Gawedz... more We define stochastic pants, and the stochastic parallel transport over them for the Felder–Gawedzki–Kupiainen line bundle over the loop space. It is related to the construction of stochastic integrals, where we cannot use martingale theory in order to define them. We get a stochastic fusion of the two line bundles when the two loops meet.
We give the definition of a line bundle over the Brownian bridge by using its section. This allow... more We give the definition of a line bundle over the Brownian bridge by using its section. This allows us to define a Hilbert space of sections of a line bundle over the Brownian bridge associated to the transgression of a representative of an element of H3(M;Z). We consider the case of a string structure over the Brownian bridge: this allows
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