Derivatives, Products, and Pullbacks in Forman's Combinatorial Differential Forms

Authors

  • Vu Quang Huynh VNU-HCM University of Science, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam
  • Thach Phu Nguyen VNU-HCM University of Science, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam
  • Phuong Van Phan VNU-HCM University of Science, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam

DOI:

https://doi.org/10.3126/jnms.v3i1.32997

Keywords:

Combinatorial Differential Form, Exactness, Product, Anti-Commutativity, Pullback

Abstract

We study derivatives, closedness, and exactness of 0-forms and 1-forms in the theory of combinatorial differential forms constructed by Robin Forman. We give an example of a closed but not exact 1-form on a non-simply connected domain. We give a sufficient condition on the domain for a closed 1-form to be exact. We show that the product of forms proposed by Forman is not anti-commutative. We propose a definition of pullbacks of forms and show that this operation has several properties analogous to pullbacks on smooth forms.

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Author Biographies

Vu Quang Huynh, VNU-HCM University of Science, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam

Faculty of Mathematics and Computer Science

Thach Phu Nguyen, VNU-HCM University of Science, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam

Faculty of Mathematics and Computer Science

Phuong Van Phan, VNU-HCM University of Science, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam

Faculty of Mathematics and Computer Science

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Published

2020-11-22

How to Cite

Huynh, V. Q., Nguyen, T. P., & Phan, P. V. (2020). Derivatives, Products, and Pullbacks in Forman’s Combinatorial Differential Forms. Journal of Nepal Mathematical Society, 3(1), 7–16. https://doi.org/10.3126/jnms.v3i1.32997

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Articles