Saturday 20 April 2024

From Gromov-Witten invariant to quantum cohomology ring and Gromov-Witten potential, in the centre considered homological mirror symmetry

 

From Gromov-Witten invariant to quantum cohomology ring and Gromov-Witten potential, in the centre considered homological mirror symmetry



From Author;
This essay is translated by Google.
So there seem ambiguous expressions in the sentences
I beg your pardon. 


From  Print  2012, Chapter 15He considered the direction of his work. Create a concise model. The model is represented graphically. Figures are expressed geometrically. Following Kenji Fukaya, geometry was defined as ``a set of groups and the spaces in which they act.'' The appeal of Fukaya's books was that they allowed us to constantly check and look at fundamental things like this.



By referring to Jacobson's "semantic minimum" and setting a geometric "minimum unit of meaning" meaning minimum, and moving time t in a closed interval, we can create a geometric concept that encompasses time as meaning. Defined the word word. He repeated this direction many times, at different geometric levels.

The universality of language approaches the invariant of mathematics. I learned from Fukaya's book that a quantum cohomology ring can be obtained from a Gromov-Witten invariant, and a Gromov-Witten potential can also be obtained. Language has become closer to mathematics and physics. Symmetry, which has long been a concern, can now be precisely inspected. At the centre of this was Koncewicz's homological mirror symmetry. 
Source: Tale / Print by LI Koh / 27 January 2012 Reference: Mirror Language / 10 June 2004 Reference 2: Gromov-Witten Invariantational Curve /27 February 2009 Homology Structure of Word / 16 June 2009 Potential of Language / 29 April 2009-16 June 2009

Source: Tale / Print by LI Koh / 27 January 2012 

Reference:
Mirror Language / 10 June 2004


Reference 2:
Gromov-Witten Invariantational Curve /27 February 2009 

Homology Structure of Word / 16 June 2009
Potential of Language / 29 April 2009-16 June 2009

References 3:
Mirror Symmetry Conjecture on Rational Curve / 27 February 2009


Kitayama Iris Park, Higashikurume, Tokyo
26 June 2014

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