TY - JOUR
T1 - Evaluation of Euler number of complex Grassmann manifold G(k,N) via Mathai-Quillen formalism
AU - Imanishi, Shoichiro
AU - Jinzenji, Masao
AU - Kuwata, Ken
N1 - Funding Information:
We would like to thank Prof. M. Yoshinaga and Prof. Y. Goto for valuable discussions. Research of M.J. is partially supported by JSPS KAKENHI Grant No. JP17K05214 .
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/10
Y1 - 2022/10
N2 - In this paper, we provide a recipe for computing Euler number of Grassmann manifold G(k,N) by using Mathai-Quillen formalism (MQ formalism) [9] and Atiyah-Jeffrey construction [1]. Especially, we construct path-integral representation of Euler number of G(k,N). Our model corresponds to a finite dimensional toy-model of topological Yang-Mills theory which motivated Atiyah-Jeffrey construction. As a by-product, we construct free fermion realization of cohomology ring of G(k,N).
AB - In this paper, we provide a recipe for computing Euler number of Grassmann manifold G(k,N) by using Mathai-Quillen formalism (MQ formalism) [9] and Atiyah-Jeffrey construction [1]. Especially, we construct path-integral representation of Euler number of G(k,N). Our model corresponds to a finite dimensional toy-model of topological Yang-Mills theory which motivated Atiyah-Jeffrey construction. As a by-product, we construct free fermion realization of cohomology ring of G(k,N).
KW - Grassmann manifold
KW - Grassmann variable
KW - Schubert calculus
KW - Supersymmetry
KW - Topological Yang-Mills theory
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U2 - 10.1016/j.geomphys.2022.104623
DO - 10.1016/j.geomphys.2022.104623
M3 - Article
AN - SCOPUS:85134608875
SN - 0393-0440
VL - 180
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
M1 - 104623
ER -