Some notes and papers

Notes

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(If name of author is not mentioned, it’s a note written by me. There can be some typo irrespective of authors. The blue leters contains link of the pdf/texfiles.)

• General

  • Riemann-Roch theorem and it’s application - Pdf.
  • Intersection homology introduction and application - Introduction, Properties and Application.

• Algebraic Topology

  • Simplicial and Singular homology, their equivalances by Acyclic model theorem and furthers- pdf (This is a part of my VSRP 2023 report).
  • Fixed-point theorems (Lefschetz) and Jordan seperation theorem (generalization of Jordan curve theorem)- pdf (This is also a part of my VSRP 2023 report).
  • Cohomology and Poincare duality- pdf.

• Algebra

  • Quick Highlights of Sheaf Cohomology - pdf
  • Kunneth Formula and Eilenberg-Zilber Theorem- pdf.

• Topology and set theory

  • Uncountable ordinals - pdf.
  • One point compactification and an example with \( \omega_1 \)- pdf.

  (These two were written in 1st year summer break)

• Analysis and convex geometry

  • Analysis III course notes (Latexed by me and my friends)- pdf and here you can find lecture wise notes.
  • Hahn Banach seperation(extension) theorems and Riesz representation theorem (Latexed by me and soumya) pdf.
  • Short notes of Lebesgue integral and Fourier Series - pdf

Papers

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The following papers/articles/notes are for my reference. It might be helpful for others too.

• Intersection homology theory by Goresky, MacPherson pdf
• Intersection homology and stratified morse theory by Goresky, MacPherson - pdf
• Rational homotopy theory by D.Quillen- pdf.
• The realization of polynomial algebras as cohomology rings by Clark and Ewing - pdf.
• Realizing certain polynomial algebras as cohomology rings of spaces of finite type fibered over \( \times BU(d) \)- pdf