🍩πŸ₯¨πŸ•³οΈ

#genus #holes #surface classification #torus #pretzel surface #algebraic topology #math

πŸ”΅βΏ

#hypersphere #n-sphere #mathematical notation #n-dimensions #algebraic topology #symbolic representation

πŸ“βž•γ€°οΈβž•βšͺοΈβž•πŸ§Š

#cell complex #attaching cells #inductive construction #algebraic topology #disk

βž°πŸ§‘βˆ—βˆ©βž°πŸŸ©

#fundamental group #amalgamated free product #pushout #group theory #algebraic topology #van kampen theorem #π₁

πŸ₯¨β†’{G}

#algebraic topology #algebraic invariants #classification of surfaces #fundamental group #homology group #topology #abstract algebra #group theory

0️⃣↗️1️⃣↗️2οΈβƒ£πŸ•ΈοΈ

#skeleton filtration #n-skeleton #algebraic topology #topological space #weak topology

β˜•βž‘οΈπŸ©Ο€β‚

#algebraic topology #fundamental group #torus #homotopy #homeomorphism #invariants #topology #abstract algebra

β˜•οΈβ†”πŸ©

#mathematical topology #homeomorphism #torus #coffee cup analogy #continuous deformation #algebraic topology

β–³πŸ”—βž•Hβ‚™

#algebraic topology #homology groups #simplicial homology #chain complex #betti numbers #topology #abstract algebra #invariants

πŸͺ’β†’πŸ”’[x]

#algebraic topology #knot theory #knot invariants #jones polynomial #alexander polynomial #topology #low-dimensional topology

βž°γ€°οΈΟ€β‚

#algebraic topology #homotopy #fundamental group #loop space #deformation retract #topology #abstract algebra

πŸ—ΊοΈβ†’

#algebraic topology #fundamental group calculation #covering space #homotopy theory #π₁ #space decomposition

πŸŸ¦πŸ€πŸŸ§β†’βž°

#fundamental group #algebraic topology #gluing spaces #path connected #π₁ #homotopy theory

UβˆͺV|U∩Vβž‘οΈΟ€β‚

#seifert van kampen #fundamental group #algebraic topology #topology notation #computing π₁ #theorem

β­•οΈπŸ©ΉβšͺοΈβž‘οΈπŸŒ•

#sphere construction #attaching disk #cell decomposition #algebraic topology #homology #homotopy

πŸ§©πŸ”—βˆ©πŸ§©β†’βž°

#fundamental group #composition law #combining spaces #gluing lemma #algebraic topology #π₁

πŸ“βž°βž‘οΈβ€’

#fundamental group #base point #nullhomotopic #contractible #topology #algebraic topology #pi_1

πŸ§±πŸ—ΊοΈπŸ•ΈοΈ

#attaching map #characteristic map #weak topology #closure finite #CW definition #algebraic topology