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This Week’s Finds

No finds this week.

 

Focus Session:

Jim delivered a talk on simplicial complexes with the primary goal of laying the groundwork for our upcoming discussion on homology. Key points from the talk included:

Introduction to Simplicial Complexes:

  • Definitions and basic examples (vertices, edges, faces, etc.)
  • How these discrete structures serve as combinatorial models for topological spaces

Motivation and Context:

  • The role of simplicial complexes in bridging combinatorial topology and algebraic techniques
  • An outline of how these ideas naturally lead into homology theory, setting the stage for further exploration in subsequent seminars

Discussion Points:

  • Questions on the nuances of complex construction and the significance of simplicial maps
  • Initial ideas on how to compute simplicial homology, emphasizing the transition from geometric intuition to algebraic formalism

 

Up Next:

Reading Group:

For next week’s reading we aim to be complete:

  • Combination of readings for Homology
    • Rotman, 3-5
    • Hatcher, 1-2
    • Lee Top, 5-6

References:

  1. Simplicial Complex: https://en.wikipedia.org/wiki/Simplicial_complex