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Yair Minsky, introduction to the mapping class groupSome surfaces of finite type.

Link #mapping class group #teichmüller #groups #surfaces #manifolds #metric #hyperbolic #geometry #topology #mathematics #maths

Heegard Floer homology by Joshua Evan Greene

Link #instantons #andreas floer #homology #cliff taubes #simon donaldson #ed witten #mathematics #maths #symplectic #surgery #paul heergard #paul heegard #topology #dynamical systems #symplectic topology #andrew casson #william thurston #henri poincaré #zoltan szabo #vladimir i arnold #joshua david greene #manifolds #surfaces #seifert surface #max dehn #knots #torus knot #homology sphere #lens space

Heegard Floer homology by Joshua Evan Greene

Link #instantons #andreas floer #homology #cliff taubes #simon donaldson #ed witten #mathematics #maths #symplectic #surgery #paul heergard #paul heegard #topology #dynamical systems #symplectic topology #andrew casson #william thurston #henri poincaré #zoltan szabo #vladimir i arnold #joshua david greene #manifolds #surfaces #seifert surface #max dehn #knots #torus knot #homology sphere #lens space

Heegard Floer homology by Joshua Evan Greene

Link #instantons #andreas floer #homology #cliff taubes #simon donaldson #ed witten #mathematics #maths #symplectic #surgery #paul heergard #paul heegard #topology #dynamical systems #symplectic topology #andrew casson #william thurston #henri poincaré #zoltan szabo #vladimir i arnold #joshua david greene #manifolds #surfaces #seifert surface #max dehn #knots #torus knot #homology sphere #lens space

Heegard Floer homology by Joshua Evan Greene

Link #instantons #andreas floer #homology #cliff taubes #simon donaldson #ed witten #mathematics #maths #symplectic #surgery #paul heergard #paul heegard #topology #dynamical systems #symplectic topology #andrew casson #william thurston #henri poincaré #zoltan szabo #vladimir i arnold #joshua david greene #manifolds #surfaces #seifert surface #max dehn #knots #torus knot #homology sphere #lens space

Heegard Floer homology by Joshua Evan Greene

Link #instantons #andreas floer #homology #cliff taubes #simon donaldson #ed witten #mathematics #maths #symplectic #surgery #paul heergard #paul heegard #topology #dynamical systems #symplectic topology #andrew casson #william thurston #henri poincaré #zoltan szabo #vladimir i arnold #joshua david greene #manifolds #surfaces #seifert surface #max dehn #knots #torus knot #homology sphere #lens space

Heegard Floer homology by Joshua Evan Greene

Link #instantons #andreas floer #homology #cliff taubes #simon donaldson #ed witten #mathematics #maths #symplectic #surgery #paul heergard #paul heegard #topology #dynamical systems #symplectic topology #andrew casson #william thurston #henri poincaré #zoltan szabo #vladimir i arnold #joshua david greene #manifolds #surfaces #seifert surface #max dehn #knots #torus knot #homology sphere #lens space

_What is a Lefschetz pencil?_ by Robert Gompf

Link #pencil #algebraic geometry #dehn twist #max dehn #kirby calculus #robion kirby #solomon lefschetz #manifolds #surgery #topology #mathematics #maths #blowing up #blowup #complex projective plane #projective geometry #singularity #singularities #fibrations #genus #surfaces #excision #4manifolds #bundles #monodromy #cylinder #torus

_What is a Lefschetz pencil?_ by Robert Gompf

Link #pencil #algebraic geometry #dehn twist #max dehn #kirby calculus #robion kirby #solomon lefschetz #manifolds #surgery #topology #mathematics #maths #blowing up #blowup #complex projective plane #projective geometry #singularity #singularities #fibrations #genus #surfaces #excision #4manifolds #bundles #monodromy #cylinder #torus

_What is a Lefschetz pencil?_ by Robert Gompf

Link #pencil #algebraic geometry #dehn twist #max dehn #kirby calculus #robion kirby #solomon lefschetz #manifolds #surgery #topology #mathematics #maths #blowing up #blowup #complex projective plane #projective geometry #singularity #singularities #fibrations #genus #surfaces #excision #4manifolds #bundles #monodromy #cylinder #torus

_What is a Lefschetz pencil?_ by Robert Gompf

Link #pencil #algebraic geometry #dehn twist #max dehn #kirby calculus #robion kirby #solomon lefschetz #manifolds #surgery #topology #mathematics #maths #blowing up #blowup #complex projective plane #projective geometry #singularity #singularities #fibrations #genus #surfaces #excision #4manifolds #bundles #monodromy #cylinder #torus

José Figueroa–O'Farrill, Spin Geometry

Link #spinors #calabiyau #sasakieinstein #eugenio calabi #shigeo sasaki #erich kähler #almost kähler #lie algebras #sophus lie #matrices #linear #manifolds #physics #Élie cartan #sphere #exceptional lie groups #sporadic groups #spin7 #even sphere #odd sphere #groups #special orthogonal group #unitary #orthogonal #mathematics #maths

José Figueroa–O'Farrill, Spin Geometry

Link #spinors #calabiyau #sasakieinstein #eugenio calabi #shigeo sasaki #erich kähler #almost kähler #lie algebras #sophus lie #matrices #linear #manifolds #physics #Élie cartan #sphere #exceptional lie groups #sporadic groups #spin7 #even sphere #odd sphere #groups #special orthogonal group #unitary #orthogonal #mathematics #maths

José Figueroa–O'Farrill, Spin Geometry

Link #spinors #calabiyau #sasakieinstein #eugenio calabi #shigeo sasaki #erich kähler #almost kähler #lie algebras #sophus lie #matrices #linear #manifolds #physics #Élie cartan #sphere #exceptional lie groups #sporadic groups #spin7 #even sphere #odd sphere #groups #special orthogonal group #unitary #orthogonal #mathematics #maths

Making matrices better: Geometry and topology of polar and singular value decompositionDennis DeTurc

Link #topology #geometry #groups #matrices #linear algebra #manifolds #lie groups #mathematics #rotation #rescaling #algebraic varieties #singular #singular matrices #submanifold #entries #projective #projective variety #projective space #kernel #tubular #boundary

Making matrices better: Geometry and topology of polar and singular value decompositionDennis DeTurc

Link #topology #geometry #groups #matrices #linear algebra #manifolds #lie groups #mathematics #rotation #rescaling #algebraic varieties #singular #singular matrices #submanifold #entries #projective #projective variety #projective space #kernel #tubular #boundary

Making matrices better: Geometry and topology of polar and singular value decompositionDennis DeTurc

Link #topology #geometry #groups #matrices #linear algebra #manifolds #lie groups #mathematics #rotation #rescaling #algebraic varieties #singular #singular matrices #submanifold #entries #projective #projective variety #projective space #kernel #tubular #boundary

Making matrices better: Geometry and topology of polar and singular value decompositionDennis DeTurc

Link #topology #geometry #groups #matrices #linear algebra #manifolds #lie groups #mathematics #rotation #rescaling #algebraic varieties #singular #singular matrices #submanifold #entries #projective #projective variety #projective space #kernel #tubular #boundary

Making matrices better: Geometry and topology of polar and singular value decompositionDennis DeTurc

Link #topology #geometry #groups #matrices #linear algebra #manifolds #lie groups #mathematics #rotation #rescaling #algebraic varieties #singular #singular matrices #submanifold #entries #projective #projective variety #projective space #kernel #tubular #boundary

Making matrices better: Geometry and topology of polar and singular value decompositionDennis DeTurc

Link #topology #geometry #groups #matrices #linear algebra #manifolds #lie groups #mathematics #rotation #rescaling #algebraic varieties #singular #singular matrices #submanifold #entries #projective #projective variety #projective space #kernel #tubular #boundary

Making matrices better: Geometry and topology of polar and singular value decompositionDennis DeTurc

Link #topology #geometry #groups #matrices #linear algebra #manifolds #lie groups #mathematics #rotation #rescaling #algebraic varieties #singular #singular matrices #submanifold #entries #projective #projective variety #projective space #kernel #tubular #boundary